The combined group, which will retain the Thomas Cook name, will be the UK's third-largest summer holiday operator, serving around 2.5 million package travellers from a network of 800 shops.
Westdeutsche Landesbank, the German banking group which owns Thomas Cook, will have a majority holding in the enlarged company, with Carlson, a Minneapolis-based US leisure corporation which owns the Radisson hotel chain, retaining a minority holding.
The company will be headed by a chairman nominated by WestLB, tipped to be Thomas Cook's current chief executive, Ulrich Zierke.
Financial details of the transaction were not disclosed as both Thomas Cook and Carlson are privately owned. Sources close to the companies said the deal would be a paper transaction with little or no cash changing hands.
Under the agreement, Carlson will add its 412 Worldchoice travel agencies to Thomas Cook's UK 385 shops. The new company will include Carlson's Inspirations tour operator, bought last year for pounds 42m, as well as Thomas Cook's tour operators Sunworld, Flying Colours and Thomas Cook Holidays.
The two groups will also link Thomas Cook's 14-strong fleet of Flying Colours aircraft with Carlson's 18-strong Caledonian Airways to form the UK's second-largest holiday airline behind Thomson's Britannia. Thomas Cook's worldwide operations, including its successful travellers' cheques unit, will also be part of the group.
The new Thomas Cook will have around 18 per cent of the UK summer holiday market, just behind market leaders Thomson and Airtours. It will employ more than 20,000 people worldwide, including around 4,300 Carlson staff.
Dr Johannes Ringel, the chairman of Thomas Cook, said the deal "would allow the company to strengthen our position in the UK and enhance our position in one of the world's largest industries".
City analysts said the deal would give Thomas Cook the critical mass to compete with Thomson and Airtours. "Travel is a high-volume, low-margin business. It's a case of having to get bigger in order to keep pace with what's going on in the sector," said David Pope at broker Wise Speke.
Industry experts said the deal would put pressure on First Choice, now the only one of the big four tour operators without a travel agency network. In recent years the market has undergone a phase of vertical integration, with tour operators buying travel agencies. The consolidation left Thomson with the Lunn Poly outlets and Airtours with Going Places.
Peter Long, First Choice's managing director, hinted that the company was poised to buy a travel agent. "We have a distribution strategy and we will make an announcement before the end of the year."