The decision follows a controversial interview in which the 37-year-old criticised the club and said he had "no respect" for manager Erik ten Hag.
Both parties stated that Ronaldo's exit was "mutually agreed".
"The club thanks him for his immense contribution across two spells at Old Trafford," said a Manchester United statement.
They wished "him and his family well for the future" and added "everyone at Manchester United remains focused on continuing the team's progress under Erik ten Hag and working together to deliver success on the pitch".
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 had just over seven months remaining on his £500,000-a-week contract with United and 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," said a statement from Ronaldo.
"I love Manchester United and I love the fans, that will never ever change. However, it feels like the right time for me to seek a new challenge.
"I wish the team every success for the remainder of the season and for the future."
Up for sale
Meanwhile, United's owners the Glazer family say they are considering selling the club as they "explore strategic alternatives".
The Americans bought the Old Trafford outfit for £790m ($1.34bn) in 2005.
It comes after years of protest from fans against their ownership.
A statement from the club said the board will "consider all strategic alternatives, including new investment into the club, a sale, or other transactions involving the company".
It added that the process "will include an assessment of several initiatives to strengthen the club, including stadium and infrastructure redevelopment, and expansion of the club's commercial operations on a global scale" to enhance "the long-term success of the club's men's, women's and academy teams, and bringing benefits to fans and other stakeholders".
In 2012, the Glazers sold 10% of their holding via a stock listing and have sold further shares in the following years.