What is more, the deal comes with a blessing - from the Keswick family, the powerful Hong Kong patriarchs eager to exit from an ill-judged foray into Trafalgar four years ago. None of the acrimony this time, no more of the unwelcome "Viking raider" headlines that surrounded Tonseth's abortive, pounds 375m swoop on rival contractor Amec last December.
The former lawyer turned-corporate-troubleshooter readily admits that the experience was a "baptism of fire" into the unfamiliar workings of the City of London. He has only one regret - the outcome - and confidently denies that the far larger Trafalgar, with activities ranging from oil engineering to the Cunard cruise line, might just be a deal too far.
"We are sorry we did not succeed with Amec. I was surprised it came to an unfriendly situation. I thought the industrial logic was good," Tonseth says. "But Amec was the second priority; Trafalgar was always first. There is a job to be done. We believe we are ready to do that job," he adds, from his office in the St James area of London.
It is an oddly salubrious setting for the no-frills Norwegian who does not even have his own secretary back in Oslo, but conveniently central for a man who spends much of his time jetting between the two cities and around the rest of the world.
Tonseth, who turns 50 this August, was born in Drobak, a tiny Norwegian town just south of the capital on the banks of the Oslofjord. Home life tells a modern Norwegian story: his wife, Mette Landgraff, keeps her surname and they only married in 1982 on the birth of their second child. Now they have three: two boys and a girl, with time for little else, bar cross- country skiing: "It's good for the mind and the body," he says.
The family, though, also avows roots over here: until the turn of the century, it was known as the Scot-Tonseths, after a Scottish mercenary who founded the paternal line. The soldier of fortune, the saga goes, was the only survivor from a band in the service of the Swedish king, who were massacred by Norse rebels in a woodland ambush.
Tonseth's father had an altogether more upright profession: as a senior High Court judge in Norway. Tonseth chose to follow in his father's footsteps, against the family's advice. In his mid-20s, he found himself as an assistant judge, presiding over anything from hold-ups to family disputes. Within a year, it had all proved too much.
"The worst were the divorce cases, deciding on who should get the children. It was terrible. At the age of 25, you don't feel qualified in the human dimension to do that," he says.
So he switched to business. His first break came in 1973 in the legal department of Norsk Hydro, Norway's biggest industrial concern. There Tonseth got his hands dirty in a spell lasting 17 years, first in the oil division, developing business in difficult parts of the world such as Vietnam, then as head of Norsk Hydro's fertiliser business where he masterminded a European acquisition spree, which included Fisons fertilisers in the UK.
"It was a huge challenge, building up the biggest fertiliser business in the world. You've either got to get big, or get out of the business. That's the challenge for companies in many areas," he says, with a clear eye on both Kvaerner and Trafalgar.
By now part of Norway's "great and good", Tonseth joined Kvaerner as a non-executive director in 1988 and leapt at the chance to be his own boss when the current job came up in 1990.
At the time, Kvaerner was still very much a federation of mostly Norwegian oil and gas businesses, technically strong and each running its own operation. The word means "mill' in Norwegian, an echo of the group's first association with timber back in the early 19th century, which continues with wood- pulp machinery manufacturing today.
The group first got into shipbuilding in 1870, hydroturbines in 1922 and oil equipment in 1966 when development of the North Sea started in Norway. Until then, Kvaerner had remained a loose collection of co-operating businesses and only in 1967 was an overall holding company created.
Since Tonseth's involvement, Kvaerner has cut its dependence on the North Sea and expanded aggressively, in shipbuilding in particular, building a world-leading position in certain sectors for very little outlay.
It is not Kvaerner's first UK move. In 1988, it rescued the Govan shipyard in Glasgow and Tonseth has since invested more than pounds 100m in oil and gas activities from Aberdeen to Croydon and hydro-electric power equipment in Doncaster. The UK now employs 3,500 of the group's 30,000 employees in all, a balance that is set to change dramatically when Trafalgar's 34,000 staff come on board.
The biggest achievement so far, though, Tonseth says, has been making sure Kvaerner's parts all gel together. It is a task he relishes at Trafalgar, where the Keswicks were tardy in getting to grips with the fiefdoms that slowed radical surgery.
"The most difficult was changing the culture. But from a personal point of view, that was the most enjoyable," Tonseth says. "Trafalgar is a similar challenge ... but we've done our homework and feel we're not risking Kvaerner."
The market took some convincing but has come round to his way of thinking. Kvaerner's shares wobbled when the deal was announced, worried about the resulting debt mountain and Trafalgar's appetite for cash.
They have since been heading on an upward tack, but doubts still remain. Tonseth is widely reckoned to have worked wonders for Kvaerner, but the stock took a battering last year after repeat profit warnings on the wood- pulp side, and has had its fair share of troubles, like Trafalgar, in contracting.
Tonseth's empire-building at Norsk Hydro, bold but somewhat risky, has also yet to bear fruit after a series of restructurings, brokers say.
"Generally, he is perceived as an aggressive leader. Kvaerner is quite good at expanding its business, but can be criticised for not having the capacity for the day-to-day running," said analyst Tomas Wold at Scandinavian broker Enskilda Securities.
To make the merger work, Tonseth also has to complete a pounds 1bn disposal programme. Assets such as Kvaerner's 23 per cent stake in Amec and 17 per cent holding in Bergesen, Norway's biggest shipping line, may be easy to offload. Cunard, though, has long been up for sale and may be a tougher nut to crack. The fleet needs huge investment and, after the QE2's disastrous cruise last year, will test Tonseth's deal-making skills to the limit.