Justin Bieber Pursued Selena for Months, and it Took Some Convincing

Justin Bieber was the one who pursued Selena Gomez, not vice versa, and it took some convincing on his part to prove to her reigniting the relationship would be a good thing.

Sources connected to both Justin and Selena tell TMZ, Selena's life-threatening medical emergency -- which ended successfully with a kidney transplant -- refocused Justin. As one source put it, Bieber didn't know how much she still meant to him until he realized she could die ... and that made all the difference.

Justin pursued Selena while she was still in a relationship with The Weeknd, although that relationship had been fizzling for months.

As TMZ reported, Selena's family was adamantly against her getting back with Justin, calling him "vile" and blaming him for Selena's severe bout of depression that landed her in rehab.

As one source put it, "Selena had to be won over." She had her doubts, but Justin was persuasive.

There have been some reports that Justin's relationship with Selena is rooted in music and not romance ... in other words, it's good business for the 2 of them to get together and collaborate on songs. Our sources says Justin and Selena are not collaborating in any way.

One thing's for sure ... they're full on back together.