The midfielder signed a two-year deal with the Ibrox club this week.
Barton rejected the opportunity to stay at promoted Burnley, as well as allegedly ignoring offers from other Premier League clubs, in order to move north of the border and join the Gers on their return to the Scottish Premiership.
The 33-year-old admitted his delight at the move on his social media accounts on Tuesday, and Rangers assistant boss David Weir insisted that the club had surpassed everyone's expectations, including their own, by sealing the signing of the former England star.
Barton has now told talkSPORT that he has not chosen the move north because he feels as though his top-class career is coming to an end; on the contrary, he insisted that he is on an "upward curve" and that his personal ambition is to be recognised as the best player in Scotland.
The midfielder said: "I still feel I can more than hold my own, I feel like I’m on an upward curve as a player as last season showed. I don’t want to go up there as a swansong, a last hurrah. That’s not me.
"I’m going up there to play the best football at the peak of my powers, challenge for titles, cups and also after getting a personal accolade this season at Burnley, I want to go to Scotland and be the best player in the country - that’s my aim.
"There’s some good players and a lot of players will want to have a say. That is something for me to aim at but it’s something I know my character will thrive on."
As alluded to by Barton, he makes the move to Rangers on the back of a fine personal season, at the end of which he was named Burnley's Player of the Year and was voted into the Championship Team of the Year by his fellow professionals.
He is now clearly hoping to take Scotland by storm, and will relish the idea of helping to lead Rangers back to the forefront of Scottish football after their four-year absence from the top flight.