Gul will go to Yerevan to attend a football match between the two countries, which do not have diplomatic relations and remain deeply divided over Armenia's international campaign to have the massacres classified as "genocide".
"A visit around this match can create a new climate of friendship in the region," the Turkish presidency said in a statement.
"It's with this in mind that the president has accepted the invitation."
The two countries will face off in a qualifying match for the 2010 World Cup finals and Armenia's President Serge Sarkisian invited Gul last month to attend.
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Published by Mike Hitchen, Mike Hitchen Consulting