Former Manchester United striker Solskjaer has found life difficult at Cardiff since replacing the popular Malky Mackay in January.
Cardiff find themselves in the bottom three, with last weekend's win over relegation rivals Fulham just Solskjaer's second league victory since he took charge.
Bellamy has been impressed by Solskjaer despite their struggles at the wrong end of the table and he is confident the Norwegian will get things right.
"I have the utmost respect for what Malky did at this club and what he did for me as a person," Bellamy told Wales Online. "I adore the man and will always be grateful.
"It's very difficult to judge a manager straight away but Ole is a very good manager. I think that will show over the next few years.
"He has been positive. Personally, I admire the way he goes about things. It's a completely different style to the last manager but he's putting his own stamp on things.
"I had a lot of respect for him as a player. He's come into a difficult situation here, but he wants us to keep believing and keep showing our character. We will do everything we can to do that."