The club parted company with former boss Malky Mackay in December following months of speculation and unrest, with Solskjaer taking charge for the first time in January's FA Cup third round win at Newcastle United.
Poor relations between Tan and Mackay were widely reported and, after Saturday's 2-1 home win over Norwich City, the owner told reporters of his delight at Solskjaer's performance.
"I am very happy with Solskjaer," he said.
"He's much better than Malky Mackay. It was a very excellent win."
Saturday was Cardiff's first Premier League win with Solskjaer in charge, coming after three successive defeats, and the Norwegian was instrumental in turning the result around, sending on Wilfried Zaha in the first half to add to his side's attacking threat.
Zaha arrived on loan from Manchester United on transfer deadline day and the change had an undoubted impact, with the winger setting up Craig Bellamy for Cardiff's equaliser after going a goal behind early on.
One major sticking point in the relationship between Tan and Mackay was reportedly a perceived failure of the Scot's big money signings' performance levels, and it was another of Solskjaer's recruits, Kenwyne Jones, who scored the goal that sealed Cardiff's first league win in eight matches.
