Arsenal made two offers for Russo, 24, in January -- one of which included a world-record fee -- but both bids were turned down by United, who hoped to keep their star striker but saw her become a free agent this summer after contract talks broke down.
"I'm really excited to be here and I can't wait to get going," Russo said in a statement. "I want to win trophies -- as does everyone in this club. I can't wait to get stuck in and grow as a player. It's a new challenge and a new environment."
Russo has been prolific in the Women's Super League, but was also a key figure in England's Euro 2022 triumph last summer. She held the role of impact substitute and managed to score four goals in the tournament, including a memorable backheeled goal against Sweden in the semifinals.
"I think the growth of the women's game has been incredible, but particularly at a club like Arsenal." Russo added. "The sell-out against Wolfsburg at the Emirates last season was fantastic, and I'm just really excited to be part of this club."
Russo started her career in Chelsea's academy before moving to the U.S. to play college football at North Carolina Tar Heels.
On her return to England, she signed for United in 2020 -- the club she supported as a child -- and went on to score 26 goals in 59 appearances. At international level with England, she has 11 goals in 21 matches.
Information from ESPN's Mark Ogden contributed to this story.