The 28-year-old will officially join the Dons when his current Tannadice deal expires.
The news was welcomed by new boss Derek McInnes, who expects the Irishman to have a big part to play next season.
He told the club's website: "I've always been a great admirer of Willo and he's a player I am looking to make a real impact for Aberdeen next season.
"With his extensive SPL experience, he was voted player of the year for Dundee United last season, which speaks volumes about his ability.
"We are delighted to have him on board as we look towards building a squad capable of bringing success back to the club."
- Sports & Recreation