Bassey has signed a four-year contract at Craven Cottage with the option to extend for a further year.
The 23-year-old Italian-born defender only joined Ajax from Rangers last summer and made 39 appearances in all competitions in his only season at the Johan Cruyff Arena.
He becomes Fulham's second summer signing following the acquisition of striker Raul Jimenez from Wolverhampton Wanderers earlier this week.
"I know how big of a club Fulham is. They always have quality players," Bassey told Fulham's official website.
"They’re playing in the Premier League, the best league in the world, so I didn’t have to think much about it.
"It’s a London club as well, so it’s always a plus to go home!
"I’m happy it’s all done now and I can just focus on the football and help the team build on last season, when they did amazing."
Fulham's sporting director Tony Khan said: "I'm thrilled to welcome Calvin to Fulham.
"He's a young and versatile defender — a homegrown player who developed at Leicester's academy before moving on to play for Rangers and then for Ajax, as well as Nigeria's national team.
"Calvin's been a top target for us, so we're all delighted that he's committed for the long term with Fulham.
"W're looking forward to watching him progress."
Fulham finished 10th in the Premier League last season.
Bassey has won 10 caps for the Nigeria national team.
