MOSCOW—Russian officials greeted President-elect Donald Trump’s choice of a Russia-friendly executive as secretary of state as an opportunity to reboot U.S. ties and push for an end to punitive economic sanctions.

Mr. Trump’s pick, Exxon Mobil Corp. Chief Executive Rex Tillerson, built his name on deals with Russia; President Vladimir Putin awarded him Russia’s Order of Friendship for his work here. He has opposed the sanctions imposed in response to Mr. Putin’s annexation of Crimea in 2014 and support for an antigovernment rebellion in eastern Ukraine.

The appointment of Mr. Tillerson portends “profound changes in U.S. foreign policy” that would be guided by pragmatic U.S. interests, rather than the idealistic pursuit of a human-rights and pro-democracy agenda, said Fyodor Lukyanov, head of the Council on Foreign and Defense Policy, which advises the Kremlin.

Mr. Trump, too, has signaled the advent of a working relationship with Mr. Putin. Yet, despite hopes in Moscow for rapprochement, U.S. and European Union sanctions on Russia remain in place. European officials say the bloc’s governments have already decided that the failure of Russia to implement the Minsk agreements with Ukraine to halt the fighting mean EU sanctions will be rolled over.

A decision is expected on Thursday. German Chancellor Angela Merkel and French President François Hollande said on Tuesday they would seek to extend the sanctions, while countries including Italy, Greece and Hungary have long opposed them or questioned their effectiveness.