Blackman, who has never played for Chelsea at first-team level, has spent the last few seasons out on loan. He played 42 games for Wycombe in League Two in 2016/17 and gained Championship experience last season after turning out 31 times for Sheffield United.
The Croydon-born stopper has also played abroad in his young career after spending a few months of 2015 on loan with Swedish club Östersunds FK.
With last season's number one Andy Lonergan leaving the club at the start of July, Leeds have confirmed that Blackman has arrived to compete with 21-year-old Bailey Peacock-Farrell for the number one spot under new manager Marcelo Bielsa in 2018/19.
Blackman joins Stamford Bridge colleague Lewis Baker at Elland Road after the Chelsea midfielder arrived on loan at the club earlier this summer.
Baker earned first-team experience during two successful seasons with Vitesse Arnhem between 2015 and 2017 and played his first year of Championship football last season with Middlesbrough.