The Red Devils have gone from strength to strength since his appointment, winning 14 of their 19 matches under the Norwegian and reaching the quarter-finals of the Champions League.
United’s renaissance under their former striker prompted the club to appoint him as Mourinho’s permanent successor on Thursday morning.
The 46-year-old, who won his first eight games in a row, has penned a three-year contract at Old Trafford.
Neville has been one of Solskjaer’s most vocal supporters and was shocked it took United so long to give him the reins.
“I thought United would take the international break to appoint Ole,” he tweeted a few hours before Solskjaer's appointment.
“I’m not sure what the plan is now.”
The former United defender wanted the club to announce Solskjaer’s appointment today so as not to draw attention away from the team’s final matches of the season.
Gary Neville (left) and Ole Gunnar Solskjaer (right) (Image: GETTY)
Gary Neville's tweet a few hours before Ole Gunnar Solskjaer's appointment (Image: TWITTER)
I thought United would take the international break to appoint Ole
Gary Neville on Twitter
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He added: “Games coming thick and fast so no ideal time to announce without a big distraction to matches.
“Let’s hope for a snap announcement today!!”
Like Neville, Solskjaer’s old United team-mate Andy Cole reckons ‘The Baby-faced Assassin’ has earned the right to manage the club permanently.
Ole Gunnar Solskjaer has signed a three-year deal with Manchester United (Image: GETTY)
"When he came to the club I could see why they were doing it, but we've got to be all brutally honest - I don't think anyone could have sat here and said he would do as well as he has.
"He has gone in, he has galvanised the club, they've got results at the right time.
"Fair enough, they have lost the last couple, but I just think he is trying to get Manchester United playing the way they used to play - attractive football, scoring goals and being entertaining. His staff have had a lot to do it with as well. Bringing Mike Phelan back was essential."
Solskjaer is delighted to have been given the opportunity to guide United back to glory, which he's 'dreamed of doing' for a long time.
Ole Gunnar Solskjaer has guided Manchester United to the quarter-finals of the Champions League (Image: GETTY)
Solskjaer will become full-time United boss says Neville
“From the first day I arrived, I felt at home at this special club," he said in a statement on the club's official website.
"It was an honour to be a Manchester United player, and then to start my coaching career here. The last few months have been a fantastic experience and I want to thank all of the coaches, players and staff for the work we've done so far.
"This is the job that I always dreamed of doing and I'm beyond excited to have the chance to lead the club long-term and hopefully deliver the continued success that our amazing fans deserve.”
Manchester United will be back in action on Saturday afternoon, welcoming eighth-placed Watford to Old Trafford.