Though it's a first-time NHL job for the former nine-year player, Ellis spent the past four years working at Sabres-affiliated Academy of Hockey as a development coach before eventually becoming the director last year.
Adams was previously involved with the academy, taking over as GM in June after Jason Botterill and a majority of his staff and scouts were fired as part of a cost-cutting purge.
Ellis, who retired following the 2014-15 season with Buffalo, also played for Detroit and Los Angeles, and appeared in 356 NHL games. The Sabres, who did not advance to the qualifying round in the Eastern Conference bubble, will pick No. 8 in the first round of the upcoming NHL draft.
The Associated Press contributed to this report.