The two-time World Cup winner played with Manchester United in the Women's Super League during the 2020-21 season but saw her time in the league cut short after she sustained an ankle and then a knee injury.
She had signed a one-year deal with the Manchester club and announced at the end of the season that she wouldn't be returning.
"Tobin's record speaks for itself. She's an incredibly talented player who will bring so much experience to our squad," head coach Jonas Eidevall said in a statement.
"This is an exciting time for the club, and I'm delighted we could secure Tobin's signing as we prepare to kick off the new season at Emirates Stadium on Sunday."
Arsenal face defending champions Chelsea in their opening game.
Heath, who is a life-long Arsenal fan, returned to fitness in time to compete with the USWNT at the Olympics where they won a bronze medal.
Her National Women's Soccer League rights are held by new expansion team Racing Louisville.
The 33-year-old has 177 international caps and has scored 35 goals in a career that has seen her win two World Cups, two Olympic gold medals and an Olympic bronze.
Arsenal come into the 2021-22 season with a fresh looking side after a number of changes. Jill Roord, Danielle Van De Donk and Lisa Evans all left the squad while the club reinforced its forward line with Nikita Parris and Mana Iwabuchi.
After Joe Montemurro left at the end of last season, Eidevall was appointed to take over.