"I'm excited about joining the set-up at the Scarlets and playing in Europe next season. It's a great team and I'm proud to be joining it," said Popham.
The player won the last of his 10 Wales caps against Japan in the November internationals. He has been training with Wales' Six Nations squad this season, but has failed to make the starting XV or win a place among the replacements.
"He is a versatile back row player and will further strengthen our squad," said Scarlets chief executive Stuart Gallacher. "This is good news for the Scarlets, we're delighted to bring him back into Welsh rugby."
The signing will boost the Scarlets, with injuries having forced the retirement of Wales and Lions number eight Scott Quinnell.