Wulff and Polish opposite number Bronislaw Komorowski laid wreaths at the Warsaw monument inaugurated in 1948 where the doomed Jewish fighters had made their last stand.
During a visit to Poland on December 7, 1970, Brandt fell to his knees at the same monument.
"I was 11 years old, but I was deeply marked by Willy Brandt's great gesture, a sign of remorse, sadness and shame in the face of the huge suffering inflicted by Germans on eastern Europe," Wulff said earlier during a meeting with young Poles.
Besides being seen as a plea for forgiveness for World War II, Brandt's gesture also came to symbolise his drive to rebuild ties with eastern Europe, which earned him the Nobel Peace Prize in 1971.
Anti-Nazi activist Brandt, a Social Democrat, spent the war in exile in Scandinavia. A fixture in post-war German politics, he was chancellor from 1969 to 1974. He died aged 78 in 1992.
Pre-war Poland was Europe's Jewish heartland. Its Jewish community numbered some 3.2 million, or around 10 percent of the country's total population. Polish Jews represented around half of the six million victims of the Holocaust.
After invading Poland in 1939, the Nazis isolated Jews in ghettos, before beginning a systematic campaign of mass murder.
On April 19, 1943, they began liquidating the Warsaw ghetto, where just 60,000 people remained after the vast majority of the 450,000 held there had died of hunger or disease or had been sent to death camps.
It was then that hundreds of poorly-armed paramilitaries in the ghetto rose up, in Europe's first urban revolt against Nazi Germany. Against all odds, they held out for three weeks.
Wulff and Komorowski also laid wreaths at a monument to the 1944 Warsaw uprising.
Around 18,000 Polish fighters and 200,000 civilians died in that failed revolt, in which Warsaw was all but razed by the Nazis.
Wulff and the liberal Komorowski also pledged to boost Polish-German ties, which have got back in track after a frosty period from 2005 to 2007 when a conservative, nationalist party was in power in Warsaw.
They also said they wanted to inject new momentum into the Weimar Triangle, a forum set up in 1991 which groups France, Germany and Poland - the latter has growing clout in the European Union, which it joined in 2004.
Wulff said the Weimar Triangle would hold a summit in Warsaw in February, with German Chancellor Angela Merkel and French President Nicolas Sarkozy set to attend.