Rossi stunned the MotoGP paddock at Valencia when he announced his decision to drop Burgess, who had been alongside him throughout his top-class career, which produced seven world titles prior to his recent barren spell.
Galbusera spent the last two seasons with BMW's World Superbike programme, but had worked for Yamaha from 1995-2011, primarily in its Superbike and Supersport teams, where he had a key role in Ben Spies' 2009 WSBK title.
Team boss Massimo Meregalli said he was confident Galbusera was the right man to take Burgess's place.
"Having worked with him personally for 10 years I have the utmost respect for his skill and technical expertise," said Meregalli.
"For sure he will need some time to adjust to MotoGP but I have no doubt that he has the capability to successfully lead Valentino's crew into and through the 2014 season."