Friend said: "The fact she hasn't been invited by the military may signify the beginning of a working arrangement between Mr Gul, who obviously has strong Islamic roots and the military, who see themselves as the guardians of the secular state."
Senior generals had earlier boycotted the president's swearing in-ceremony, widely-seen as a sign of protest against their new commander-in-chief.
Critics have accused Gul and the AK party of pushing an "Islamist agenda" but the president has insisted he will maintain Turkey's separation of religion and state.
On Wednesday, Gul approved a cabinet with a mix of AK party and secular members aimed at pushing stalled political and economic changes necessary to win entry to the EU.
The 25-member cabinet includes eight new members, and has strong business credentials.
In July, the ruling AK party won a sweeping election victory but was unable to form a government until now due to objections by Ahmet Necdet Sezer, Gul's secularist predecessor.
Gul's original candidacy in April had also sparked months of political turmoil in Turkey after secularists opposed the move.
Friend said: "Turkish politics after the election of a new president, the announcement of a new cabinet, is slowly getting back to normal."
"But clearly, these tensions that we've seen will bubble away under the surface."