At Portugal, he replaces Fernando Santos, who spent eight years in charge and led them to their first major title at Euro 2016.
"I'm very happy to be here, I'm delighted to be able to represent one of the most talented teams in the world," Martinez told a news conference on Monday.
"From the first time I met the board and the president, I knew that this was the project I wanted. I understand that there are high expectations and goals, but I also understand that there is a large group of people working to meet our goals."
Portugal were eliminated from the World Cup at the quarterfinal stage in a 1-0 defeat to Morocco, in which Santos made the bold call to bench Cristiano Ronaldo for a second straight game. Santos later said he had "no regrets" about the decision.
When asked about Ronaldo's future role with the national team, Martinez said: "Decisions have to be made on the pitch. I'm not a coach who makes hasty decisions. I want to meet everyone, and starting today, I want to talk and get to know all the players.
"Cristiano is part of that list, he spent 19 years with the national team and deserves respect, let's talk. From there, it's up to me to make the best list for the European Championship. Tomorrow we'll start working, getting to know all the players, and Cristiano is one of them.
"We are going to start a footballing process to try to get to know all the players that could be part of this selection. We are going to give all the players an opportunity and respect all those who are already in the squad. Cristiano is one of them. It's a process that we have to face naturally, with responsibility, and we're going to make important decisions for the team."
"We were looking for a coach that is ambitious, knowledgeable about international football, used to training players at the highest level and with experience in major leagues and national teams," Portugal's FA president Fernando Gomes said.
"The place of birth of the new coach was never relevant. We have players who have played, play or will play in different leagues. Roberto Martínez's path speaks for itself. He has built a career based on work and the acquisition of skills. Six years ago, he started to coach Belgium and took them to No. 1 ranking in the world."
ESPN's Adriana Garcia also contributed to this report.