The 33-year-old was the club's player of the season and was also voted the players' player of the year.
"I can't thank my team-mates enough for letting me do what I do," the utility back told BBC Radio 5 live.
Gopperth's brilliant score against Northampton was also named try of the season.
The former Newcastle Falcons player also picked up the Golden Boot award for scoring 221 points during the campaign.
"I am only one cog in this massive organisation. The way the boys play encourages me and makes me want to be better," he added.
Gopperth's coach Dai Young won the director of rugby award. His side  topped the regular season table.
Lichfield's England international Harriet Millar-Mills was named women's Premiership players' player of the year for the second season.
Wasps' Jimmy Gopperth has been named the Premiership player of the year to complete a hat-trick of awards.