Turkey’s PM Ahmet Davutoglu said the remains of Suleyman Shah would be moved elsewhere in Syria.
He said troops had destroyed the tomb’s complex, apparently to prevent it from being used by Islamic State (ISIS) militants.
Turkey considers the shrine be to sovereign territory.
Suleyman Shah was grandfather of the founder of the Ottoman Empire, Osman the first.
“We had given the Turkish armed forces a directive to protect our spiritual values and the safety of our armed forces personnel,” Ahmet Davutoglu said in televised remarks.
Earlier, in a series of tweets, Ahmet Davutoglu hailed the armed forces for carrying out a “highly successful” operation amid the “inherent risks” of conflict in Syria.
He said the remains had been moved to Turkey but would soon be rehoused in an area of Syria under Turkish military control, closer to the Turkish border.
The Turkish flag had already been raised over the site, Ahmet Davutoglu said.
There were no clashes with ISIS during the operation, but one soldier died in an accident, he added.
The operation began on Saturday at about 21:00 local time and ended on Sunday morning.
A large convoy, including 600 troops and almost tanks and armored vehicles, passed through Kobane – the city which Syrian Kurdish fighters retook last month from ISIS – and travelled some 20 miles south to the tomb on the banks of the Euphrates river.
Suleyman Shah is believed to have drowned in the river.
The tomb has been permanently guarded by a contingent of about 40 soldiers, who rotate periodically. The site is part of Turkish territory, according to a treaty signed in 1921.
The Turkish convoy was believed to be larger and more heavily armed than usual because of recent heavy fighting between the Kurdish militia and Syrian rebel groups against IS militants.
Since driving ISIS out of Kobane in January, the Kurdish Popular Protection Units and rebels have taken a number of surrounding villages.
They are now said to be only 15 miles from Tal Abyad – the strategically important border town east of Kobane that is used by ISIS militants to cross into Turkey.
ISIS has seized large swathes in Syria and Iraq, proclaiming a caliphate.
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