The record-breaking forward marked his return to the Premier League with two goals in United's 4-1 win over Newcastle, and Solskjaer relished the feel-good factor around the club.
Speaking after their emphatic win - which also featured goals from Bruno Fernandes and Jesse Lingard - Solskjaer told the BBC: "I'm so happy for Cristiano. I'm so happy for the team and supporters. You sense the atmosphere around the club since he signed. It could easily have been an anti-climax because expectations were so high.
"It feels like one of the old days. It's special. Cristiano Ronaldo is a special man and a special player for us in the history of the club.
"He senses big moments and scores goals. He's clinical, he's ruthless. He's lifted the team and everyone around the club.
"Everyone is dreaming. [The fans] can dream and we'll focus."
Ronaldo's two-goal return also drew praise from former Newcastle striker Alan Shearer.
The Premier League legend admitted to being wowed by the 36-year-old star.
Shearer - who was still playing when Ronaldo joined United as a teenager - said after the match: "Ronaldo punished Newcastle.
"Sometimes you've got to applaud someone. He's been great for such a long time. To come in and do what he has done today - do what he's been doing all his career - is phenomenal.
"You've got to hold your hands up and have huge respect for him. He keeps on going and going. There doesn't seem to be an end in sight."