Graham Potter has been looking to bolster his attacking ranks with a shortage of forward options available to him. Armando Broja is set for a spell on the sidelines after being stretchered off during a friendly defeat against Aston Villa in Abu Dhabi.
Fofana, an Ivory Coast international, will join the club on Jan. 1 for a reported fee of $13.15 million (£10.93m).
Fofana made his debut for the Ivory Coast national team in a 4-0 friendly win against Burundi in November.
The striker has enjoyed a fruitful recent season with Molde in the Eliteserien, the top flight of Norwegian football, contributing 15 goals and five assists in 24 matches. He also scored four goals in 10 appearances in the Europa League conference qualifiers and main tournament this campaign.
Chelsea marked their return to Premier League action with a comfortable 2-0 win over Bournemouth on Tuesday. Kai Havertz played as striker for Potter's side with Pierre-Emerick Aubameyang dropped to the bench.
The London club are eighth in the Premier League and have scored the fewest number of goals of any side in the top 10.
Information from Reuters contributed to this report.