Sousa jumped ship from his role as Poland boss to take over at Flamengo at the end of last year.
The former Portugal midfielder signed a two-year deal, but has been relieved of his duties following back-to-back Serie A defeats for the Rio de Janeiro giants
Flamengo are languishing in 14th place after they were beaten 1-0 by Bragantino on Thursday, a loss that came following a 2-1 defeat to Fortaleza.
Polish FA president Cezary Kulesza accused Sousa of being "disrespectful" after he left his role as Poland head coach to move to Brazil.
Sousa had been in charge of Bordeaux before taking the Poland job.
Former Portugal midfielder Sousa replaces Jerzy Brzeczek, who was surprisingly relieved of his duties on Monday.
Brzeczek was sacked despite Poland's qualification for Euro 2020 as Group G winners, having won eight of their 10 qualifying matches.
Sousa has been out of work since leaving his role as Bordeaux boss last August and was linked with the Juventus job before Andrea Pirlo landed the role.
The 50-year-old's appointment on Thursday came less than five months before Poland's first game of the rescheduled European Championship, with Slovakia their opponents in a Group E contest on June 14.
Sousa said: "I am honoured and proud to be the coach of the Polish national team. At the beginning, I would like to thank president [of the Polish Football Association] Zbigniew Boniek and the entire management board for the fact that I can take up such a great challenge.
"Poland is a country of football and I am convinced that your enthusiasm will give us strength, support and faith in the representation. Together, we will be able to fight for victories at the European Championship.
"With the right mentality, discipline, organisation and approach, together with me, my staff, federation employees and the support of the entire nation, we will be strong. I am sure that all of Poland will be proud of its national team."
Sousa only landed the Poland job in January after the dismissal of Jerzy Brzeczek.
The former Portugal midfielder asked to vacate his position earlier this week, having received an offer from Brazilian club Flamengo
Polish FA president Cezary Kulesza described Sousa's request to jump ship as being "extremely irresponsible" before a decision was made to terminate his contract.
Sousa was confirmed as Flamengo boss soon after his exit from the Poland job was announced and Kulesza made his feelings over the 51-year-old's conduct very clear.
"Working with the Polish national team is a great honour and privilege," Kulesza said in a statement.
"Therefore, we could not agree to such a disrespectful approach by the coach to the players and co-workers, and above all to the millions of fans for whom the national team is sacred.
"The function of the coach of the Polish national team must be performed by a person who, apart from appropriate experience and skills, has respect for this position.
"We treat this situation as a valuable lesson for the entire football community in order to properly arrange cooperation with the new coach from the very beginning."
Sousa, meanwhile, revealed his joy and excitement at Flamengo, who finished second in Brazil's Serie A this year.
"This is a message addressed to the greatest fans in the world," Sousa said to Flamengo's official website. "I [have] great pride and satisfaction in representing a club of incomparable beauty like Flamengo.
"It is time now to work hard to give joy and titles to the 40 million fans around the world. We will play and win together."
