Pogba and Lingard announced their departures on Wednesday, with the club confirming Matas exit on Thursday when his contract expires in June.
The club said: “Thank you for dedicating eight years of your career to United, Juan. Everyone at the club wishes you all the best for the future.”
In a video message recorded on the Old Trafford pitch, Mata said: “I wanted to say thank you very much to all of you for your support over the years and especially during the difficult times that we lived together.
“I will never forget you, thank you very much. All the best, from the bottom of my heart and goodbye.”
Pogba had confirmed his departure on Wednesday, writing: “I feel privileged to have played for this club.
“Many beautiful moments and memories but most importantly an unconditional support from the fans. Thank you.”
Pogba joined United in 2016 from Juventus for a then-world-record fee of 89.3 million pounds, having spent time at the club from 2009 to 2012.
The France international made 226 appearances and scoring 39 goals in his second stint at Old Trafford. He won the Europa League and League Cup with United in 2017.
Lingard has been linked with a return to West Ham United after a successful loan stint in 2020-21.
He wrote on social media: “Born and bred a red. Over the last few weeks, I’ve been emotional about leaving a club that is family. After 22 years Ive had so many special memories and moments that I will cherish forever.
“@ManUtd will always remain in my heart. A massive thank you. Lots of love Jlingz.”