The forward, who's signed a two-year deal, joins the Blues after spending nine years at Scottish Women's Premier League side Hibernian, where she made her debut aged just 15 in 2019.
In her first full season in 2020/21, her performances earned her the Scottish Women's Premier League Young Player of the Year Season award.
Last season, Adams scored 14 goals and assisted three more in 24 games, earning the club's Staff Player of the Year award.
She said: "I wanted to take that next step in my career and after talks with the manager (David Wright) it just felt like the right place for me to do that.
"It’s my first time away from home and Ipswich seems like a really nice place to be so I’m really excited to get going."
Sean Burt, Town Women's technical director, said: "Eilidh is a fantastic signing for us and has been a proven goalscorer for a number of years.
"She is a senior international and league-winner who brings a magnitude of experience for a player entering her prime years."
Adams is the seventh signing of the summer for the Tractor Girls.
The other six are:
Midfielder Jenna Slattery from Hearts
Midfielder Aimee Palmer from Southampton
Winger Rosie Livingstone from Hibernian
Winger Megan Hornby from Portsmouth
Forward Kit Graham from Spurs
Centre-back Georgia Hunter from Hearts