The 20-year-old, who can also operate as an attacking midfielder, had been on Albion's radar for several weeks before the deal was concluded, with a substantial sell-on clause included in the agreement.
Morgan spent last season on loan at Peterborough United in League One, scoring 14 goals in 39 appearances in all competitions.
He began his career at Southampton before joining Chelsea's academy in August 2023, making six appearances and scoring once for the Blues' Under-21s before spending the second half of 2024-25 on loan at Gillingham.
Morgan said his conversation with head coach James Morrison had convinced him of the club's ambitions.
"My conversation with the manager was good. He told me about the style of football he wants to play and how I'm going to fit into that," Morgan said. "He also spoke about the work he wants to do with me to help bring out my best attributes. I've heard nothing but positive things so far and I understand how big the club is."
He added that the move had come together swiftly once Albion made their intentions clear.
"I heard of Albion's interest about two weeks ago. The club moved things on and we managed to get it all agreed pretty quickly," he said.
The England youth international arrives at The Hawthorns as one of Chelsea's more promising young forwards, and West Brom will be hoping that his record at Peterborough — 14 goals in 39 appearances in League One — translates into a similar impact in the Championship.
Morrison's side finished in mid-table last season and will be looking to close the gap on the division's top clubs, with Morgan viewed as a player who can contribute immediately rather than one requiring a lengthy period of adjustment.
Excerpt (207 chars): West Bromwich Albion have signed Chelsea striker Jimmy-Jay Morgan for around 4 million pounds on a four-year deal, with the 20-year-old having scored 14 League One goals for Peterborough on loan last season.