The 45-year-old has experience first hand of both players, having coached at MK Dons when Tavernier was at the club on a loan spell, as well as being involved with sides that featured against Waghorn on more than one occasion.
And the ex midfielder said he thought both players had proved themselves at a decent enough level to suggest they would be fine acquisitions by the Gers.
"I'd be delighted if Rangers signed James Tavernier and Martyn Waghorn," Rae said in the Mail ahead of confirmation of the move. "They are both very fine players and can make a really good impact.
"They have both played many, many games at a good level in England and they would settle in right away."
It was a sentiment echoed by Scotland international Don Cowie, who has just finished a season with the pair at Wigan, and he told the Daily Record that the Glasgow giants had managed to sign two "great players".
Cowie, who also played with Rob Kiernan, before the defender's move to Rangers earlier in the summer assured Gers fans that just because Wigan went down to the third tier of English football last season, it didn't mean the former Wigan trio were weak players.
“They both have good pedigree," he is quoted as telling the Record. "Trav has been part of promotion-winning sides in the last two years. He helped Rotherham get up then did it again at Bristol City last year. He came through the ranks with Newcastle and is a very good young player.
“Waggy is the same. He was at Sunderland and Leicester before joining Wigan. He’s a bit older but it was hard for everyone here last season. We were all gutted with relegation.
“He is a player who’ll reward you with goals if he gets a run of games. I’ve played against him and he is a real handful. He has great movement and is dangerous in and around the box."
The former Inverness star also revealed that he had a little chat to the players once news Rangers were interested came to light.
“When I heard there was interest from Rangers I spoke to them," he added. "They’ll soon see how big a club they are signing for. They’ll see it for themselves in this week’s friendly with Burnley.
“They will soon know what they have got into and, all going well, this time next year they will be preparing for the Premiership.
“Most people down here know Rangers are still a huge club even though they are not in the top flight at the moment.”