Slade’s excellent form contributed to Exeter being in with a chance of reaching the Premiership play-offs going into their final match at Leicester, however, defeat by the Tigers and results elsewhere meant Chiefs eventually finished seventh.
He recently agreed a new contract with the Devon club, ending speculation that he may move to France.
Slade was left out of England’s Rugby World Cup squad before the campaign began, but started all five matches of England’s Six Nations campaign earlier this year and now has 62 caps for his country.
Winger Feyi-Waboso, 21, made his international debut during the Six Nations, having opted to represent England over his native Wales.
He beat Harlequins duo Fin Baxter and Chandler Cunningham-South, and Newcastle flanker Guy Pepper, to claim the breakthrough player award.
Other prizes announced at the ceremony in London included Saracens’ Andy Christie being named community player of the season and a special recognition award for Wayne Barnes, who ended his refereeing career after officiating South Africa’s Rugby World Cup final victory over New Zealand in October.