Santos, 68, was in charge of the Selecao for over eight years and guided them to success at Euro 2016 and the inaugural Nations League in 2019.
Despite those trophies, Portugal fans had become frustrated with the style of football Santos' team played in recent years, with there being a perception of him underachieving given the wealth of talent at his disposal.
Santos' Portugal contract was not due to expire until after Euro 2024, but he was removed from his role after the World Cup quarter-final defeat to Morocco last month.
Roberto Martinez has since replaced him.
Santos has not wasted much time in taking a new job either, however, with Poland his third international position in succession after also coaching Greece for four years prior to taking over Portugal.
He will be only Poland's third non-native head coach after Portuguese compatriot Paulo Sousa, who had a brief spell in charge in 2021, and Leo Beenhakker.
Polish Football Association (PZPN) president Cezary Kulesza had essentially confirmed the hiring on Monday when he posted a photo of himself with Santos, the caption announcing a press conference for the following day.
Santos' first goal will be to secure Poland's qualification for a fourth successive appearance at the European Championship, with the 2024 edition to take place in neighbouring Germany.
He will then be tasked with leading Poland to the 2026 World Cup in Canada, Mexico and the United States, after which his contract is due to end.