The Republic of Ireland Under-21 international, who can play at right-back or in central defence, will go straight into the Glovers’ squad for their FA Cup clash with Bradford on Saturday.
The 20-year-old, yet to make a competitive debut for the Reds, is Yeovil’s second January acquisition after midfielder Jared Bird moved to Huish Park from Barnsley on Thursday for the remainder of the campaign.
Whelan wrote on his Twitter account: “Delighted to be joining @YTFC on loan until the end of the season All the best to all players and staff @LFC for the rest of the season.”
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.
RB Leipzig came from behind at the Red Bull Arena to end a run of four winless games and defeat Bundesliga leaders Bayern Munich 2-1 on Sunday.