Morata scored 20 goals in 43 apperances in all competitions last season for Madrid after returning from Juventus, but was allowed to leave the club by Zinedine Zidane.
With Diego Costa set to depart Stamford Bridge, the 24-year-old is set to be Antonio Conte's first-choice striker and former team-mate James believes he can flourish in the role.
"Morata is an amazing player with an amazing strike," the new Bayern Munich signing told reporters.
"He will do very well at Chelsea. At Real Madrid, he was very good."
Bayern boss Carlo Ancelotti also expects Morata to impress at Chelsea, believing that Conte has made a fantastic signing by bringing the Spain international to the Premier League.
"He is a fantastic striker and young too. Chelsea have a made a good signing," Ancelotti said.
"He can help the team to be better. He is a complete striker. At Real Madrid, he played as a central striker, on the side sometimes and in all attacking positions.
"He is a really good signing. He can work a lot for the team also."