The Sun claims the two actors had a tearful heart-to-heart after Kristen was spotted in a clinch with married father-of-two Rupert Sanders.
"They pretty much decided they couldn't live without each other," a source told the newspaper.
"Kristen poured her heart out to Robert and told him it was a one-off and a mistake.
"Rob sees it as Kristen made a really stupid mistake. After a lot of long tearful talks, they've worked it out."
Twilight's star couple are now said to be rebuilding their love nest in Los Angeles.
Robert initially packed his bags and moved out of the mansion they shared while he contemplated their future together.
The positive development seems to confirm Kristen's recent claim that things were "totally fine" with her estranged boyfriend.
Regardless of what happens behind the scenes, fans will see the pair reunited as they join forces to promote The Twilight Saga: Breaking Dawn Part 2 in November.