The 19-year-old becomes Darren Moore’s third signing of the summer so far, following the arrivals of Jason Lokilo and Josef Bursik respectively.
Hammersmith-born Richards - who spent a spell at Fulham as a schoolboy - joined Albion last summer from Manchester City, having impressed in their under-23s side during the 2018-19 Premier League 2 campaign – scoring 10 goals in 29 appearances.
He moved north to City as a 14-year-old and featured for the club through to under-23 level, with Pep Guardiola naming him on the bench for City’s Carabao Cup semi-final clash with Burton Albion in January 2019.
He switched to Brighton that summer, moving for an initial fee of £1million, with add-ons potentially taking the package to £2.5million.
Richards made his full senior debut in their Carabao Cup defeat at Aston Villa last season and was a regular for Brighton’s U21 side in the EFL Trophy last season and scored in the win over Southend United.
On Richards' move to Doncaster, Albion technical director Dan Ashworth said: "This move is a great opportunity for Taylor to get some good senior experience in a competitive League One environment with Doncaster Rovers.
"We will be monitoring his progress closely and wish him all the best for the season ahead.”
Richards could make his debut for Rovers in their Carabao Cup tie at Blackburn on Saturday.