Manchester United reached their first final of his tenure with a Europa League last-four triumph over Roma.
A 6-2 first-leg victory at Old Trafford meant United already had one foot in the Gdansk final ahead of the trip to Italy.
However, Roma made things uncomfortable and won an entertaining semi-final second leg 3-2.
Solskjaer piled praise on Cavani who followed his first-leg double with another two goals in Rome.
“The reason we’re here is because we’ve got a centre-forward who has scored four goals during the tie,” Solskjaer said.
“Edinson has shown again why we want to keep him at Old Trafford.”
“Football has its own language.”
“Edinson has proven tonight, in previous games and throughout his career what a centre-forward should be doing both on and off the ball both preparing for games and recovering from games.”
“He’s an absolute top professional and everyone in my team can learn from him.”
United made it to Europa League final to set-up a shot at glory against Villarreal in Poland on May 26.