WASHINGTON — Jon M. Huntsman Jr. has accepted President Trump’s offer to be ambassador to Russia, people with knowledge of the matter said on Thursday, taking on a diplomatic assignment that would be challenging in the best of times but is more so now, given the questions swirling around the Trump campaign and its links to Russia.

Mr. Huntsman, a former Republican governor of Utah, served as former President Barack Obama’s ambassador to China from 2009 to 2011. Experts said he will need his political dexterity to navigate Moscow at a time when Mr. Trump has called for better ties even as Russia’s role in the 2016 presidential election remains under intense scrutiny.

“Not only is there this mess with the investigation that will complicate his assignment, there’s a lot of incoherence within the Trump administration regarding its policy toward Russia,” said Michael A. McFaul, who was ambassador to Russia in the Obama administration.

The F.B.I. is known to have examined possible contacts between Russia and Trump advisers. Congress also has opened an inquiry.