Solskjaer led United to 10 wins from his 13 Premier League games as caretaker manager, losing only once, elevating the club into the race for Champions League football.
United also made history under Solskjaer by overturning a 2-0 first-leg home deficit in their Champions League last-16 tie against Paris Saint-Germain, to reach the quarter-finals where they face Barcelona.
Beckham, who spent seven years as Solskjaer’s team-mate at United, believes the Norwegian is the right man to take the club forward.
“It’s great he has done an incredible job, so he deserves the contract he has got,” Beckham told Sky Sports News, speaking at the Bahrain Grand Prix.
“He is loved by the fans and the players and everyone else at the club. He has done a great job and it will continue because real fans love him. It’s great for the club and great for him.”
Beckham has also been impressed by Gareth Southgate, another of his former team-mates, since he has taken over as England manager, praising his selection of young players.
“It’s exciting. I was excited when Gareth took over because I think he spent enough time with the players from a very young age,” added the former England captain.
“To see them go into the first team squad and the way they are playing – it is exceptional to see.
“I think it does not matter how old they are – we’ve all talked about age over the years – but when they’ve got the experience they’ve got playing for the teams they play for it does not matter what age they are.
“If they are playing the way they are – it is exciting times.”