Thomson, Boro manager Gordon Strachan's seventh signing from the Old Firm, has signed a four-year deal with the Championship club.
The central midfielder began his career with Hibernian before moving to Ibrox in 2007 in a £2m deal.
The midfielder has suffered two serious knee injuries in his career, the most recent being in November 2008, but on each occasion Thomson has fought his way back to full fitness and first-team football.
And he was a near ever-present last season as Rangers picked up a league and Co-operative Insurance Cup double.
Former Celtic manager Strachan praised his new signing's mental strength.
"Kevin knows the game and he's got great determination about him, very much in the Barry Robson mould," he told Middlesbrough's official website.
He is going into the last year of his contract and, from the player's point of view, Middlesbrough can maybe offer more long-term security than he can have here
Rangers manager Walter Smith
"He's also a more disciplined player than most but he isn't just a sitting midfielder.
"He's a very good passer, he retains the ball well and he scored some important goals in Scotland. He's an excellent signing."
Rangers manager Walter Smith admitted last week that the debt-hit club were not in a position to offer new deals to players unless they are in the final few months of their contracts.
So he has opted to cash in on Thomson instead of risking losing the player for nothing next summer.
"We have had difficult decisions to make and hopefully it will work out for all concerned," Smith told Rangers' official website.
"I did say last week that we had number of players going into the final year of their contracts and that we might have to look at offers if any came in.
"That was followed by headlines that we are selling all of our players, but we're not and we don't have to sell a player.
"However, there are two sides to the Thomson deal in that he is going into the last year of his contract and, from the player's point of view, Middlesbrough can maybe offer more long-term security than he can have here.
"So we have that to take into account for all players and that's what's happened in the case of Kevin.
"We have had difficult decisions to make before and hopefully it will work out for all concerned."
Smith had hoped to bolster his midfield with Burnley winger Chris Eagles.
But the player has rejected the chance of a move to Glasgow after his wage demands were not met.
Source: BBC Sport
Source: BBC Sport