For the last decade, Saturday Night Live's "Weekend Update" has been co-anchored by the show's head writer — first with Tina Fey (2000 to 2006) and then Seth Meyers from 2006 until now. With Meyers taking over Late Night from Jimmy Fallon (himself a former "Weekend Update" anchor), the tradition continues: SNL head writer Colin Jost will co-anchor "Weekend Update" alongside Cecily Strong.
Jost joined SNL as a writer in 2006 and became a head writer in 2012, a title he shares with Rob Klein and the soon-departing Meyers. Jost's first show as co-anchor is March 1st. Late Night with Seth Meyers begins the Monday prior, February 24th, and The Tonight Show Starring Jimmy Fallon will begin one week before that on February 17th.
More succinctly: Jost is taking over for Meyers is taking over for Fallon is taking over for Leno is retiring (again).