The Spain international has been in impressive form after being drafted in from Real Madrid for around £75m.
He has bagged three goals in his first four Premier League appearances, including one against Leicester in the Blues’ 2-1 win on Saturday.
And Drogba says grabbing goals early in the season will boost Morata’s confidence enormously.
“He’s scoring goals. On his first game where he came off the bench, he scored even though the team lost,” Drogba told Sky Sports News.
“Now he is scoring goals that are winning games so I am really happy for him and for the club as well.
"It is very important to score. For a striker it’s even more important to score because when you start with a new team, people have high expectations.
"When you match those expectations, you are just happy and the goals continue to come.
"I hope he will have a great, great season because we need that."
N’Golo Kante grabbed Chelsea’s other goal in Saturday’s clash with Leicester.
And Drogba was full of praise for the diminutive French midfielder.
"I was proud that he scored his goal,” Drogba added.
“It was a very difficult game. It is always difficult to play at Leicester so I am happy with the result."
