The quartet will appear on the morning show's summer concert series on Aug. 31 in Central Park.
Richardson announced he was leaving the group in 2006, but has appeared in the lineup occasionally since. The remaining Backstreet Boys - Nick Carter, Howie Dorough, Brian Littrell and AJ McLean - announced Richardson would be rejoining them permanently during a performance in London last April.
A statement says all five are in a London studio with producer Martin Terefe working on a new album that will be released next spring to coincide with the group's 20th anniversary.
Carter says the group "couldn't be happier to have our brother back with us."