Tindall brought Woodgate into the south-coast club during his time as Cherries boss, before he was sacked after six months in charge.
Tindall, a close friend of United’s chief executive Stephen Bettis, has joined Paul Heckingbottom and Alan Knill at Bramall Lane after Wilder’s departure last weekend.
And Woodgate, speaking to the Bournemouth Echo, said: "I’m really pleased for Jason.
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"I think at times when something like that happens at a club you’ve been at for a long time and are emotionally connected with, I think it’s good to get back in straightaway.
"That’s what Jason’s done. He’s been a manager here and an assistant to Eddie Howe.
"He’s gone there to help the coaching team out and I think it’s brilliant for him to get back in the game.
"He’s a really talented manager, a really talented coach who has been there and done it so it’s a no brainer. But I’m so pleased that he’s back in."
Tindall had a watching brief at the King Power Stadium as United were hammered 5-0 by Leicester in United’s first game without Wilder at the helm, and officially began his new role this week.
"It is a privilege to be asked to be involved and I'm looking forward to getting started,” Tindall said.
“I've previously worked with a couple of the players before and have experience at this level, which I hope will be of benefit to Paul and the team."