Ajeti, 23, joins the Scottish champions on a four-year deal for a fee of around £5m (€5.5m).
Hail Hail from our new number 🔟! 💪🍀
— Celtic Football Club (@CelticFC) August 13, 2020
The plan had been for Ajeti to initially join Celtic on loan, but the clubs instead negotiated a permanent deal.
The 10-time Swiss international made just nine substitute appearances for the Hammers in his debut campaign.
Celtic boss Neil Lennon expressed his delight at signing Ajeti.
“We are delighted to bring Albian to Celtic,” said Lennon. “He is a tremendous player, an international with real quality and I know he is really determined to do all he can to bring more success to our supporters.
“I have admired him for long time as he is a really intelligent footballer, well balanced and a really good finisher.
“We are so pleased to make him a Celtic player and we hope he has a long and prosperous career with us.”