The 18-year-old travelled to south Wales on Monday night and trained with his new team-mates on Tuesday, with the move ratified by the Premier League that afternoon.
McEachran, who joined Chelsea at the age of eight, revealed he chose Swansea ahead of other Premier League clubs, saying: "I'm delighted to be here."
He added: "I wanted to come earlier but Chelsea had a few injuries and things. There was interest from a number of other Premier League clubs but I wanted to come to Swansea because of the style of football they play. I think it will suit me."