The Belgium international is set to join Chinese Super League club Shandong Luneng after the two clubs agreed a fee for the 31-year-old on Thursday.
Fellaini signed a new two-year contract at Old Trafford last summer, but Osman thinks the change in style under Solskjaer since Jose Mourinho’s sacking in December has made a departure the best option.
“I would say he was more accustomed to a Jose Mourinho style of football,” Osman told BBC Radio Five Live.
“He’s physical, strong, effective at both ends, whereas Manchester United require a much more technically gifted player than unfortunately Fellaini’s capable of.
“Effective... that’s the word for his time at Manchester United, but you can understand why Ole Gunnar Solskjaer feels him surplus to requirements and I think for all parties it would be best if he found himself elsewhere.
“He’s a nice fella. He took a while to learn the language but a really nice fella, desperate to get involved in the dressing room.
“He really did bring an awful lot to the dressing room as well. He’s one of those players you thought you could rely on and you could turn to him in a desperate situation.
“I feel now, even at United, he won’t be one of those players that will ruffle the dressing room and upset the way things are going.
“I think he will get on with his job as a professional but he will want to play football before his career ends.”
Fellaini joined United in 2014 for £27 million, becoming the first significant signing of the post-Alex Ferguson era, and has scored 22 goals in 177 appearances for the club.
