Schwan, 65, will run for the second time against German President Horst Köhler, a Christian Democrat, in the May 2009 election. Köhler, a former head of the International Monetary Fund, narrowly beat Schwan in 2004.
On Monday the centre-left Social Democrat (SPD) candidate appealed for votes from the hard-line Socialist party The Left, which has gained support at the SPD's expense in the past year.
"Whoever choose to vote for me from The Left has chosen in favour of constructive politics and for democracy," Schwan said.
The widely expected nomination has dominated headlines in Germany for days.
After Köhler announced he would run again last week, members of his conservative Christian Democrats (CDU) said their coalition partners the centre-left Social Democrats (SPD) should not have their own candidate for head of state. Chancellor Angela Merkel's coalition with the SPD has been in place since fall 2005.
Merkel recently described the situation within the coalition with the SPD as "very, very difficult."
But Social Democrats said it is the right of every party to have their own candidate for the presidency.
The German president plays a largely ceremonial role, although Köhler was called on to adjudicate in 2005 as to whether the then SPD Chancellor Gerhard Schröder's decision to dissolve the lower house of the German parliament, the Bundestag, and call early elections was constitutional.
Parliamentary elections will take place in September 2009, shortly after Köhler's current term expires in May 2009.
The conservative newspaper Frankfurter Allgemeine Zeitung wrote that Schwan's nomination was seen by Merkel's party as a provocation and predicted that it will keep tensions high right up to the national vote: "We are looking at a protracted election campaign that will run from now until September 2009."