Ranieri, who arrived at the London club a month before Solskjaer returned to Manchester but who has struggled to have anything close to the same positive effect as the 45-year-old, said: "At the moment he deserves it".
However, a number of supporters couldn't quite understand the club's thinking, taking to social media to express their concerns.
'Sincerely hope this is just to get value when he is sold SOON! tweeted another. Only versus Arsenal (5) and Charlton (4) has Ranieri lost four consecutive Premier League games versus a single opponent. I've supported United for many years since I went home. His existing contract was set to expire this coming summer.
"I am delighted to have signed a new contract", he said.
'I've got a picture of what this Man United team should look in a couple of years, I don't know if it's with me, but I put my views to Ed and the club'.
'I am excited about the challenges that lie ahead of us as we prepare for a very busy period in the season. He has won the Premier League, FA Cup and Europa League at Old Trafford, and has made 27 appearances for England.
Finally, unlike Ince, Solskjaer is a legendary figure at the club and is revered by all United fans who remember that fateful day when the baby-faced assassin scored the victor in the Champions League final and secured us the treble.
"Any footballer would say the same thing, [my goal is] to win as many titles and trophies as possible, as much silverware as possible and it is also really important to keep developing, progressing and improving as a player over the years".
That one-sided victory was followed by away losses to Valencia and Liverpool which brought about the demise of Mourinho, and since then Ole Gunnar Solskjaer has led the Red Devils to nine wins and a draw in 10 games, with spirits raised and fans thrilled along the way.