Jones has been out of action for the last 20 months due to a troubling knee problem.
The former Blackburn Rovers defender’s last appearance for the Red Devils came in an FA Cup tie against Tranmere Rovers in January 2020.
The 29-year-old has been building up his fitness with matches for Manchester United’s reserve side and has now been cleared to take his place in the first team.
"I'm so happy for Phil," Solskjaer told MUTV. "He has completed two 90 minutes for the Under-23s, played some minutes behind closed doors and he's got no reaction on his knee.
"He's been working really hard. I've been part of that myself and had the best part of three years, or at least more than two out of three years, and I know what challenges he's been through, mentally, thinking 'will I ever play football again or even be able to walk again and be able to play with the kids in the garden'.
"He's been so diligent and so professional; no frills, no social media and I'm old school. I like players like that. He just focuses on one thing and gets his head around the challenges and he's back.
"He will be in the squad. It’s a good day for him and for us, and it’s something that he has earned."
Man United defeated West Ham 2-1 in the Premier League last Sunday.
