Slightly less than a quarter (24 percent) of respondents remained opposed to same-sex couples being given legal equality.
With 68 percent in favour, support has grown by around 3 percent on this issue since YouGov last conducted the poll less than 12 months ago.
Across the political spectrum, Germans said they wanted to see a change in the law.
A total of 61 percent of voters for Chancellor Angela Merkel's conservative Union said they were for legalization, suggesting that the Chancellor's opposition to gay marriage is now out of step with her own voter base.
Support on the left of German politics was expectedly high. Social Democrat and Die Linke (left party) voters both gave 79 percent approval to same-sex marriage, while 87 percent of Green voters were in favour.
The poll also sought to find out opinions from within church congregations - again support for equality was high.
Sixty eight percent of Catholics were in favour and 67 percent of Protestants. Within both religions, just over a quarter of respondents did not want the law changed.
Currently gay couples are allowed to enter into a civil union which entails many, but not all of the rights of a heterosexual marriage.
READ ALSO: Five ways Germany falls short on gay rights
Homosexual couples are, for example, currently not able to adopt a child together.
But, on the question of raising children, the YouGov poll also showed most Germans believe gay couples are just as capable of raising children as straight couples.
Sixty three percent said a gay couple could raise a child just as well as a straight couple, 19 percent said they would be worse at raising them, while 4 percent thought same-sex couples would make better parents.