United announced they had reached an agreement with Juventus to re-sign the 36-year-old forward on Friday.
Personal terms have been agreed on a two-year contract, with the required aspects of the deal to be finalised before the deadline on Tuesday night.
The Premier League club will pay around €15m (£12.87m) plus a further €8m (£6.86m) in add-ons for the Portugal captain, who underwent a medical in Lisbon over the weekend.
Ronaldo scored 118 goals in 292 games during his first spell with United between 2003 and 2009.
“Hopefully we can get the paperwork sorted and announce him very soon. He is a winner and a great human being. The players are excited, and l am excited to keep adding to this squad.
“He adds something completely different. It adds more confidence and belief to what we are doing and what we are building.
“We know he is a more experienced player than he was when he was here last time, he has evolved and had an unbelievable career. I’m sure he likes all the talk about ‘he’s too old’. Make it personal and he will show what he can do.”
Solskjaer warned his Manchester United forwards Ronaldo would likely be going straight into the first team.
The Norwegian added: “He is not signing to sit on the bench. He is going to make us a better team.
“We need to get all the paperwork done, hopefully we can get that sorted and we can announce it 100 per cent.
“Then he is away with Portugal, they have three games, his last game is Tuesday (September 7) and then we can get him back to Manchester and involved as soon as possible.”