The striker, who has managed only one appearance for England (as a substitute against Cameroon) was keen to leave Ewood Park from the moment they were relegated to the Nationwide League. He attracted interest from Tottenham Hotspur, Arsenal and Aston Villa, whose enthusiasm waned when Rovers valued him at pounds 12m.
The fee is the third highest between English clubs after the pounds 15m that Newcastle United paid Blackburn for Sutton's former strike partner, the England captain Alan Shearer, and the pounds 12.6m Aston Villa received from Manchester United for Dwight Yorke.
Chelsea's striking options have been reduced by injury to the Italian Pierluigi Casiraghi, who missed most of last season with knee ligament damage, the departure of the Dane Brian Laudrup and Gianluca Vialli's decision to stop playing and concentrate on his managerial duties.
Vialli thinks the 6ft 3in presence of Sutton will add another dimension to Chelsea's play. "He can be a tough player on the pitch, which is something sometimes that we missed last season and he's got a great personality," the Italian said. "He's not a cheap player - pounds 10m is a lot of money - but I think sometimes you have to spend money if you want to improve the team and strengthen the team, and that's why we've signed him."
Sutton, relishing the chance to challenge for honours with Chelsea, said: "I'm looking forward to getting started. I just hope I can emulate those who have done well here over the years.
"It's very important coming to Chelsea now. There was a feeling about the place when I first joined Blackburn five years ago and there's a similar one here. Chelsea have got some very experienced players and hopefully I can blend in."
Sutton missed a large part of last season through injury and his absence had a major bearing on Blackburn dropping into the First Division. He made only 20 appearances, scoring four goals, and missed the final six matches as Rovers finished next to bottom.
With the 26-year-old Sutton's signature secured on a six-year contract, Vialli was able to confirm the decision he made last month to retire as a player. Not that he will ease up on himself in training. "I want to keep myself fit, even though I won't play again," Vialli said. "I want the players to know I'm with them when they work really hard, so I'm going to do it all with them.
"I'm going to stop playing so I can be a better manager and this is for the club because I would like to keep on playing. I'd like to keep on scoring goals but I want to do the best for the club," he told ClubCall. "As a manager you have to make a decision for the club and this is the time to do it."
Sutton joins the Liverpool-bound defender, Stephane Henchoz, in leaving Rovers in the wake of their relegation, but the club issued a statement yesterday that was optimistic an immediate return to the Premiership.
John Williams, chief executive at Ewood Park, said of Sutton's departure: "At the end of last season Chris Sutton made it clear that he felt the time was right for him to further his career away from Ewood Park.
"That being the case we immediately underlined our determination to secure the best possible financial deal for the now feel we have achieved that goal. The pounds 10m doubles the then British record fee we paid to Norwich City for the player some five years ago.
"No one likes to lose good players but we have an excellent squad here and believe our ambition of achieving an immediate return to the Premiership is a realistic one."
The competition for promotion will be tough and Rovers will need to make the most of their resources, but to rebuild after the demoralising decline of last season may serve them best.
Foe set for Liverpool, page 27
LEADING BRITISH TRANSFERS
TOP 10 TRANSFERS BETWEEN BRITISH CLUBS
pounds 15m Alan Shearer Newcastle from Blackburn July 1996
pounds 12.6m Dwight Yorke Man Utd from Aston Villa Aug1998
pounds 10m Chris Sutton Chelsea from Blackburn July 1999
pounds 8.5m Stan Collymore Liverpool from Nottm Forest July 1995
pounds 7.25m Kevin Davies Blackburn from Southampton Jun 1998
pounds 7m Stan Collymore Aston Villa from Liverpool May 1997
pounds 6.25m Andy Cole Man Utd from Newcastle Jan 1995
pounds 6m Les Ferdinand Tottenham from Newcastle July 1997
pounds 6m Les Ferdinand Newcastle from QPR July 1995
pounds 5.75m Nick Barmby Everton from Middlesbrough Oct 1996
TOP TRANSFERS INVOLVING BRITISH CLUBS
pounds 15m Alan Shearer Blackburn to Newcastle July 96
pounds 12.6m Dwight Yorke Aston Villa to Manchester United Aug 98
pounds 12m Juninho Middlesbrough to Atletico Madrid Jun 97
pounds 10.75m Jaap Stam PSV Eindhoven to Manchester United Jun 98
pounds 10m Chris Sutton Blackburn to Chelsea July 99
pounds 8.5m Stan Collymore Nottingham Forest to Liverpool May 97
pounds 8m Andrei Kanchelskis Everton to Fiorentina Feb 97
pounds 7.5m Dennis Bergkamp Internazionale to Arsenal Jun 95
pounds 7.25m Kevin Davies Southampton to Blackburn Aug 98
pounds 7m Stan Collymore Liverpool to Aston Villa May 97
pounds 7mi Fabrizio Ravanelli Juventus to Middlesbrough Aug 96