MOSCOW — Russian lawmakers on Thursday overwhelmingly approved Mikhail V. Mishustin as the new Prime Minister, elevating a little-known technocrat picked by President Vladimir V. Putin as part of an unexpected Kremlin shake-up.

Mr. Putin on Wednesday proposed major changes to the Russian Constitution that would spread political power more evenly, away from the president to the Parliament, the State Council and other government institutions.

Many analysts saw the potential reordering of Russia’s political system, which surprised the country’s political elite, as an effort by Mr. Putin to ensure that he remains in power past 2024, when his term ends — though how exactly that would work remained unclear.

Shortly after Mr. Putin put forward the overhaul in his annual state of the nation address, his ally Dmitri A. Medvedev resigned as prime minister, saying that it would clear the way for the proposed constitutional changes. On Thursday, Mr. Putin appointed Mr. Medvedev deputy chairman of the country’s Security Council, which advises the president.