MOSCOW—Russian President Vladimir Putin on Monday signed a law allowing him to potentially hold onto power until 2036, a move that formalizes constitutional changes endorsed in a vote last year. The July 1 constitutional vote included a provision that reset Putin’s previous term limits, allowing him to run for president two more times. The change was rubber-stamped by the Kremlin-controlled legislature and the relevant law signed by Putin was posted Monday on an official portal of legal information. The 68-year-old Russian president, who has been in power for more than two decades—longer than any other Kremlin leader since Soviet dictator Josef Stalin—said he would decide later whether to run again in 2024 when his current six-year term ends. He has argued that resetting the term count was necessary to keep his lieutenants focused on their work instead of “darting their eyes in search for possible successors.” The constitutional amendments also …