In Football News, the Spaniard, 49, replaces Fernando Santos, who resigned after Portugal's quarter-final defeat by Morocco at the World Cup last month.
Martinez stood down as Belgium coach after six years in charge following their group-stage exit in Qatar.
"I am very happy to represent one of the national teams with the best talent in the world," said Martinez.
70% - Roberto Martínez won 56 of his 80 matches in charge of the Belgian national team, his win percentage of 70% is the highest among all @BelRedDevils managers with more than one match. Iberian. pic.twitter.com/uhR0zCyxQT
— OptaJohan (@OptaJohan) January 7, 2023
"I am very excited to be here. From the first time I spoke with the president of the federation I knew this was a sporting project that would excite me.
"I understand there are great expectations and big objectives, but there is a great team of people at the federation and I have great excitement that together we can achieve those objectives."
Portugal football president Fernando Gomes said: "This is an important moment for the national team."
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Martinez spent four years as Wigan manager, which included winning the 2013 FA Cup, before a three-year spell at Everton in which they finished fifth once and 11th twice in the Premier League.
Appointed Belgium coach in 2016, he led them to the top of the Fifa rankings in 2018 after they came third at the World Cup in Russia.
Portugal won the 2016 European Championship and the 2018-19 Nations League during Santos' eight years in charge.
However, they won only one of their three group matches in Qatar and their campaign was overshadowed by Santos dropping forward Cristiano Ronaldo for the knockout matches.
Martinez himself had a World Cup to forget with Belgium, who failed to even make it out of the group stage and also had a crisis within the squad - with the Spaniard criticised for struggling to make the most of his talented group during his six-year tenure with the side.
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