Baxter, who was voted director of rugby of the year last season, led Exeter to an unlikely fifth-place finish in 2012, while Gustard has been on the Sarries staff since 2008 and has previously worked alongside Farrell.
"It's obviously a great honour to be asked to assist in the preparation of the England squad," said Gustard. "I am grateful to Saracens for giving me the opportunity to continue my development as a coach at national level."
Baxter served Exeter, who currently sit eighth in the Premiership, as a player for 14 years, 10 of them as captain, before joining the coaching staff in 2006. He oversaw their debut Heineken Cup campaign this season after guiding them to eighth and fifth-place finishes following promotion to the top flight.
"I see it as a fantastic opportunity for me to do what we keep saying to the players here at the club, which is to keep learning, keep doing better and experience new things," he said.
"This is a great chance for me to experience something different, learn from other coaches such as Stuart, Mike Catt and Paul (Gustard) and work with some different players."
England head coach Stuart Lancaster added: "It was important that we found two coaches who could mirror the skill set of Graham (Rowntree) and Andy (Farrell) while they are away and come in and keep developing the players within our system.
"Paul, having worked together with Andy at Saracens, already has a good understanding of how we operate and Rob, who has done a great job in developing a very competitive Exeter pack, will pick up the set piece and breakdown."