Ramsey will earn around £400,000 per week at Juventus, making him the highest-paid British player of all time.
In an emotional statement, Ramsey thanked Arsenal fans and vowed to give 100 per cent for the club until he leaves at the end of the season.
But club legend Wright believes Arsenal have no one to blame but themselves for losing Ramsey after letting him run down his contract.
He told BBC Radio 5Live: “Ramsey is just another player who got into a situation where he could run the contract down and when you consider the contract that have been given out, they just couldn’t afford to keep him alongside the players they’ve got with the contract that they are on.
“So, unfortunately, we lose him and he been magnificent.”
When asked if Ramsey was appreciated at Arsenal, Wright added: “Maybe not.
“But I think what people will see now is when you watch how he plays and the professionalism like David Ornstein has mentioned he’s one of those players that no matter how poorly Arsenal were playing, he never hid.
“Never hid, always showed for the ball.
“Got loads of stick from loads of people but continued to try and make things happen in the way he sees fit.
“It comes down to mismanagement. We can’t get away from that but the fact is we’re losing a great player.”
In his 11 years at Arsenal, Ramsey has made over 350 appearances in all competitions, scoring 61 goals.
He is also the only Arsenal player in the club’s history to score multiple FA Cup-winning goals.
In a 75-word statement, Arsenal said Ramsey had been a “consummate professional” in his time at the club.
Arsenal said: “Everyone at Arsenal Football Club wishes Aaron Ramsey a happy and successful future.
“Aaron’s made a fantastic contribution to our club since joining from Cardiff City in 2008.
“He has always been a consummate professional and will always have a special place in the hearts and memories of Arsenal fans around the world.
“We look forward to Aaron helping the team to a strong end to this season before he joins Juventus in the summer.”