The Serbia international turned down the offer of staying at Bremen and has instead accepted a three-year contract to join Frankfurt on a free transfer.
Frankfurt's general manager Bruno Hubner is happy to have concluded a deal to bring in the versatile 23-year-old in the summer.
"We are delighted the transfer has been agreed," Hubner told Deutsche Presseagentur.
"Despite his age, Aleksandar is already an experienced player able to shine in various positions. He is designed to play in the holding midfield role, but he could also be played in both full-back positions."
Ignjovski is not the only Bremen player to have rejected a new deal, with Aaron Hunt, who has been linked with a move to the Premier League, also set to leave in the summer.
Bremen's general manager Thomas Eichin told Kreiszeitung Syke: "I have been forced to get a decision from Aaron Hunt and discussed this with his agent.
"He told me Aaron Hunt will not agree to the offer we submitted. This is what we have to accept as a club."
However, Bremen have secured promising young defender Oliver Husing on a professional contract until 2017 and he will step up to the first-team squad at the end of the season.