Giggs, a former teammate of Solskjaer's at Old Trafford, has been impressed with the recruitment that has been made under the Norweigan's tutelage and says there are plenty of 'good characters' at the club.
"He's done really well, because it wasn't easy [going into that job]. He had a tremendous run when he first took over and then a bit of a dip," he said on the Jonny Owen & Friends show.
"I've been really pleased and happy with the signings he's made. They're not only good players, but they look like they are good characters who want to play for United.
"Maybe that [element] was missing for a couple of years, so to get that back has been great.
"Everyone is interested to see what happens now and if they can get in that top four, considering how well he was doing before the coronavirus [pandemic]."
Meanwhile, the Wales boss expressed his joy at leading his country to a second successive European Championship - and believes the postponement of the tournament until next summer could benefit his relatively young side.
"It was a great achievement by the boys after doing so well in 2016, and we wanted to get back there," Giggs explained.
"We didn't want it to just be a flash in a pan, so to get there again is amazing, but we've obviously got to wait another year for it to come around.
"I've looked at the positives of it really. We had a lot of players who were going to miss the tournament, like Joe Allen, and there were a few players lacking in game time.
"We've got a pretty young team, so them young players will be a year older and more experienced, so hopefully it will be a positive.
"Going against that we had tremendous momentum unbeaten in six games, and of course we were all geared up for this summer. But it is what it is and we'll be prepared for next summer."
Ryan Giggs has told talkSPORT that he believes Ole Gunnar Solskjaer has done 'really well' during his tenure as Manchester United boss so far.