The pair have both signed three-year contracts.
They join former Latics team-mate Rob Kiernan in moving to Ibrox this summer, along with former Hearts captain Danny Wilson and former Middlesbrough winger Andy Halliday.
Powerful former Sunderland and Leicester forward Waghorn, 25, has struck eight goals in 18 months with Wigan while Tavernier spent the second half of last season on loan with Bristol City.
The 23-year-old right-back started his career at Newcastle and has also had loan spells with Gateshead, Carlisle, MK Dons, Sheffield Wednesday, Shrewsbury and Rotherham.
Tavernier revealed the reputation of Rangers and the chance to work with manager Mark Warburton had attracted him to Glasgow.
He said: “Rangers are a massive club and as soon as there was interest there was no thinking about it. The history of the club, what they have achieved in Europe and in Scotland made it an easy decision for me.
“It is a great opportunity to play up here and the recognition that you can get playing for Rangers is huge.”
Waghorn also highlighted the influence of Warburton and assistant David Weir.
“I know the way they played with Brentford having played against them a few times,” he said.
“When I sat down with them and they got across their ideas and how they want to play, it was brilliant. It’s exactly how I want to play and how I see my football going. It was a no-brainer. I see myself being here for the long-term.”