Financial details of the transfer were not disclosed by either club, but English media reported that Ipswich paid Sunderland 15 million pounds ($19.8 million) for the player.
Clarke has scored 28 goals in 114 appearances for Sunderland. He was initially loaned from Tottenham Hotspur and made a permanent move to Sunderland in 2022.
Clarke is Ipswich boss Kieran McKenna's 10th signing in the close season.
"Kieran McKenna really sells the club and the journey it's on, as well as what they're still trying to achieve, and you're almost silly if you don't want to jump on board with the way things have been going," Clarke said in a statement.
Ipswich lost 4-1 to Manchester City on Saturday and 2-0 to Liverpool in their league opener. They host Fulham next in the Premier League on August 31st.