The 31-year-old midfielder has agreed a deal that will keep him at Man Utd until 2021, with the option for a further year.
Since joining the Red Devils from Chelsea in 2014, Mata has been involved in more Premier League goals, scoring 33 and providing 23 assists, than any other player for the club.
And with Mata also winning the FA Cup, League Cup and UEFA Europa League while at the club, Solskjaer is keen to use his experience for the younger players at Old Trafford, such as new signing Daniel James.
"He is a great example to our younger players in his approach," Solskjaer told the club's official website.
"As well as everything he brings on the pitch, we have some fantastic young players here and I know that Juan's vast experience will help them to reach their potential over the coming seasons."
Mata has made a total of 243 Premier League appearances for Chelsea and United since moving to England from Valencia in 2011.
Last season Mata claimed his 50th PL goal and 50th PL assist in the same match, as Man Utd earned a 4-1 victory over Fulham.
"I am looking forward to working with Ole and his fantastic coaching staff; the vision that they have for the club is truly exciting and I am so happy that I will be a part of that," he said.
Man Utd start their 2019/20 Premier League campaign at home against Mata's former club Chelsea on Sunday, 11 August.