The former France international's move comes after he was cleared to leave French Ligue 1 Marseille before the final year of his contract last month.
"Our number 10 has arrived! Payet has signed a pre-contract with Vasco," the Brazil side announced on social media. "He'll arrive in Rio in the coming days to have his medical and sign the contract," Vasco added.
Local media suggest Payet, 36, joins the club which has yo-yoed between the first and second divisions over the past few seasons on a deal until 2025. Payet, with eight goals from 48 appearances for France, leaves Marseille where he became a fans' favourite over two spells totalling eight seasons.
He also had a stint with Premier League side West Ham from 2015 to 2017, making 49 appearances and scoring 11 goals before returning to Marseille.