The Berliner Morgenpost newspaper judged that Steinmeier looks set to be "the anti-Trump president".
The vote was held in Berlin's glass-domed Reichstag building by a special Federal Assembly, made up of national lawmakers and electors sent from Germany's 16 states - among them deputies but also artists, writers, musicians and national football coach Joachim Loew.
The German president has little executive power but is considered an important moral authority.
In his acceptance speech, the newly elected president called Germany "an anchor for hope", and said "the country should take on responsibility and serve as a role model for other countries", Deutsche Welle reported.
However, she said he was coming to office during hard times.
In 2010, when he was Germany's main Opposition leader, Steinmeier chose to take a break from politics to donate a kidney to his wife, Elke Budenbender, a judge at Berlin's administrative court.
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Merkel congratulated him on Sunday and said she was convinced he would be an excellent president who would enjoy wide support.
Steinmeier assumes the presidency on March 19.
German local media have long speculated Steinmeier as the obvious victor, since he got the grand governing coalition as well as the influential Social Democratic Party of Germany on his back.
He has always been one of Germany's most popular politicians.
But the vote is widely seen as a test for the unity of Merkel's political coalition, as well as a prelude for Merkel's campaign seeking her fourth term in the federal election in September.