The 30-year-old had represented the Gunners for 12 years after joining from Sunderland in 2010, scoring 81 goals in 270 appearances for the North London club.
However, Nobbs has found regular starts difficult to come by in recent months, and her contract with Jonas Eidevall's side was due to expire at the end of the season.
Nobbs came up with three goals in 16 Women's Super League and Champions League appearances for Arsenal in the first half of the 2022-23 campaign, but she has now bid a fond farewell to the North London club.
Sporting director Edu Gaspar paid tribute to a 'lifelong' member of the Arsenal family, telling the club's official website: "Jordan has been a wonderful servant to Arsenal Football Club,"
"Over the past 12 years, she has written her name into the Arsenal history books and forged a deep connection with our loyal supporters. We would like to wish Jordan health, happiness and success on and off the pitch in the future - she is a member of the Arsenal family for life."
Head of Women's Football Clare Wheatley added: "Jordan has been an integral part of this football club for over a decade and her contribution and achievements are clear to see.
"She embodies what it means to be a Gunner and will go down as a true Arsenal legend. We wish her all the very best in this next chapter and look forward to welcoming her back here as our guest whenever she likes."
During her 12-year stay in North London, Nobbs won three WSL titles, four Women's FA Cups and five Women's League Cups, as well as being named the FA Player of the Year for 2016 and FA Players' Player of the Year for 2017.
The England midfielder has signed an 18-month contract with Aston Villa, with an option to extend, and manager Carla Ward believes that the club can help Nobbs force her way into the England setup.
"This is a big signing for us and Jordan is one of the country's most decorated footballers. She's a winner and will bring a wealth of experience that her new teammates will thrive off," Ward told avfc.co.uk.
"We're delighted to secure her signature and we hope this move can help the football club as well as cement her place back in the international set-up."
Nobbs has earned 69 caps for the England national team during her career and could make her debut for Villa when they return to WSL action against Tottenham Hotspur on January 14.