Born in Tonmawr, Tandy played for local side Neath RFC and then Ospreys but was not capped by Wales.
The former back row will return to Wales after coaching Ospreys between 2012 and 2018.
He won the Celtic League title in his first season in charge of the Swansea-based region.
Tandy left Ospreys for a role with Australian side Waratahs, before linking up with Scotland in 2019.
He also held a defence coach role with Gatland's British and Irish Lions squad in South Africa in 2021.
WRU chief executive Abi Tierney says Tandy was the "standout candidate" and that the Union had secured the "very best coach" for the job.
"This is a keystone appointment for us and an integral part of our five-year strategy as we look to achieve sustainable success for our senior men's side," said Tierney.
"Steve fits the bill in terms of the affinity he will be able to create with a young group of players with huge potential, but also the galvanising effect we know he can have on the whole rugby ecosystem as a proud Welshman.
"Our task now is to ensure Steve has the support and resources he needs to succeed in this role."
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