On Monday Medvedev announced that Bortnikov, who previously headed the economic security department of the Federal Security Service (FSB), was to head the FSB, leaving former chief Nikolai Patrushev to head the national Security Council.
"I am counting on Alexander Bortnikov to preserve the continuity of the service's best traditions and to continue the policy of qualitatively improving it," Medvedev told staff at the FSB headquarters in central Moscow.
The president, who assumed office last week replacing Vladimir Putin, said that among other issues Bortnikov will have focus on counter-terrorism and extremism along with measures to curb ethnic and religious intolerance.
He said that in a multi-confessional country such as Russia, attempts to undermine unity are considered a direct national threat.
"We have serious tasks ahead in the sphere of economic security, particularly the protection of the Russian economy from corrupt and criminal pressure and industrial espionage, and the strengthening of guarantees for entrepreneurship and private property," the president said.
"A focus of the FSB's work remains the prevention of illegal activities on behalf of the foreign intelligence services."
After congratulating Bortnikov on his appointment, Medvedev thanked the former FSB chief, Patrushev, for his work at the service.
"These were not the easy years, but he has achieved all set tasks honorably."
The president also said that he expected Patrushev, in his new role as head of the Russian Security Council, to make decisions to strengthen the Armed Forces, and to step up measures against corruption and terrorism.
"I believe it would be right to pay close attention to the strengthening of our Armed Forces and law enforcement bodies, and to improve the fight against crime, corruption, terrorism and extremism," Medvedev said.
Russian Prime Minister Vladimir Putin announced his new government on Monday, keeping the main ministers in their posts and bringing in several former Kremlin aides.
Putin proposed the new lineup at a meeting with his hand-picked successor Medvedev, who quickly approved the appointments. The finance, defense, interior, and foreign ministers, along with several other prominent Cabinet figures, remained unchanged.