The Norwegian was rewarded with a three-year deal after dramatically reviving United's fortunes since taking caretaker charge in December, lifting his side back into contention for a top-four place and transforming the mood at the club, AFP reported.
The highlight of his reign so far was a dramatic 3-1 away victory over Paris Saint-Germain in the last 16 in the Champions League, which enabled United to overturn a 2-0 first-leg defeat to reach the quarterfinals on away goals.
Solskjaer has given his creative players license to attack, with Paul Pogba and Marcus Rashford let off the leash to devastating effect.
But some of the gloss has come off in recent weeks, with three defeats in four matches badly denting United's chances of qualifying for next season's Champions League and dumping the Red Devils out of the FA Cup.
Solskjaer, who famously scored the winning goal for United against Bayern Munich in the 1999 Champions League final in Barcelona, was upbeat after drawing the Spanish league leader in the quarterfinals last month, before he was confirmed as the new long-term boss.
"We want these games against the biggest clubs and the biggest teams. We had the final against them in 2009 and 2011 (both of which Barca won) and the semifinal in 2008 when Scholesy (Paul Scholes) scored," Solskjaer said.
"It's these games our fans and this club crave. We are looking forward to this one."
Worryingly for Solskjaer, though, some of United's familiar failings under Jose Mourinho have returned to haunt his team in the weeks since the draw was made.
United was unfortunate to lose at Arsenal but appeared short of inspiration in losing twice to Wolves in the FA Cup and Premier League, while even Solskjaer admitted they did not deserve their solitary win since he was given the permanent job as Watford enjoyed the better of the chances in a 2-1 defeat at Old Trafford.
Solskjaer had a free ride when he took over from Mourinho, with morale at a low ebb and the club 11 points off the top four.
Despite recent hiccups, he has had notable success in his short time at the club and ultimately has his sights set higher than finishing in the top four.
"You've got to aim high," he told ESPN. "You cannot aim too low at this club. You've got to aim to win titles.
"When I came back here as the manager I thought a lot about what makes a winning team. What does it really take to win on the biggest stage? I'm not one to sit back, rest on my laurels."
The 46-year-old will probably be forgiven if United falls short against a Lionel Messi-inspired Barcelona.
But if he fails to reverse the mini-slump and United suffers a heavy defeat to the Spanish champion there is a danger the season could peter out and momentum could be lost.
Questions will be asked as to whether United was too quick to put its trust in a likeable leader and whether Solskjaer has the profile needed to bring in the top-level recruits that United needs, particularly in defense, to become serious Premier League and European challenger again.
But he will lead his team out at Old Trafford on Wednesday for its first Champions League quarterfinal since 2014 with the same never-say-die attitude he had as a player.
"We've got a chance, it's going to be a tough one. We've got a mountain to climb, but we've climbed a few mountains before," said Solskjaer.