United are fifth in the Premier League in Ten Hag’s first season as manager, with the season taking a break for the World Cup in Qatar.
Ronaldo is with Portugal at the tournament and is expected to lead them in their Group H opener against Ghana on Thursday.
He spoke to Qatari media on Monday, saying he would ‘talk whenever he wanted, and his feud with United will not ‘shake’ the Portuguese squad.
Ronaldo, who has scored 145 goals in 346 appearances for United, left Juventus to join the club from Old Trafford in August 2021 – 11 years after leaving to join Real Madrid.
He had over seven months left on his £500,000-a-week contract with United. His departure leaves him free to sign for another club, including one in the Premier League, when the transfer window opens in January.
“Following conversations with Manchester United, we have mutually agreed to end our contract early,” Ronaldo read.
“I love Manchester United and the fans; that will never change. However, now is an excellent time to look for a new challenge.
“I wish the team every success for the rest of the season and the future.”
Ronaldo, who has three goals in 16 outings for United this season, has not played because of an unspecified illness since he captained the side in their 3-1 defeat at Aston Villa on 6 November.
He was dropped for the Premier League game at Chelsea last month by Ten Hag after refusing to come on as a substitute against Tottenham three days earlier.
In his TalkTV interview last week, Ronaldo said he did not regret refusing to come on as a substitute for the final few minutes in a win against Spurs as he felt Ten Hag had “provoked” him.
He also spoke about how, in general, he felt “betrayed by the club” and, along with his view of Ten Hag, added that he thought he was being forced out of the club.
He also said he had seen “no evolution” at the club since former manager Sir Alex Ferguson retired in 2013.
Ronaldo mentioned that he was close to joining Manchester City before his return to United, while he had turned down a £305m deal to move to a Saudi Arabian club in the summer.
He talked about the loss of his baby son in April and how touched he was by a tribute paid to him by Liverpool fans at a game against United at Anfield in the days afterwards.
United responded last Friday with a statement saying they had “initiated appropriate steps” in response to the interview.
“Cristiano obviously did that interview with the mindset that he wasn’t happy and wanted to get out of the club. He clarified that,” former Manchester United defender Rio Ferdinand told BBC Sport.
“I think Erik ten Hag got what he wanted in this situation. Both parties are happy, and we can move on.
“The next chapter for Cristiano? It depends on what his motivation is. Play in the Champions League? Money? To continue playing somewhere with a nice climate?