David Tennant played the Tenth Doctor from 2005 to 2010, becoming arguably the most popular actor to play the role since Tom Baker (who played the Fourth Doctor from 1974 to 1981). Catherine Tate played his companion Donna Noble, debuting in the 2006 Christmas Special and returning regularly in Series 4 in 2008. Her last appearance came in Tennant's swansong, the special The End of Time, in 2010. Tennant's last appearance was in the 50th Anniversary special The Day of the Doctor in 2013, where he starred alongside Eleventh Doctor Matt Smith.
Returning showrunner Russell T. Davies is penning the 60th Anniversary Special, which is also expected to mark the first full episode for Ncuti Gatwa as the Fourteenth Doctor. Davies would not be drawn on how Tennant and Tate will return, encouraging speculation that it might be a dream, a flashback or a parallel universe. It's also not entirely clear if they are returning for the 60th Anniversary Special itself, or possibly a separate special or episode airing as part of the same celebrations.
It is so far unknown if the other Doctors of the modern age - Matt Smith, Peter Capaldi and Jodie Whittaker - are returning for the anniversary as well.
UPDATE: Actor Yasmin Finney (Heartstoppers) has also been cast for the 60th Anniversary, playing a character called Rose. Russell T. Davies often has characters called Rose in his drama, including the co-lead in Bob & Rose and, of course, Rose Tyler in his first stint in Doctor Who. It is unclear if this new character is a guest star or the new regular companion.