"We bonded like crazy. It was like we'd known each other forever," Lavigne, 29, tells PEOPLE exclusively. "It's a very intimate process, and you have to really open up when you're songwriting. When it was over and I had to go work with other people, it sucked. So I called him and asked him to come back to L.A. to do some more writing with me, and he was like, 'Hell yeah!' "
Soon the two had fallen for each other romantically – and written enough love ballads to fill several albums.
"We wrote a song called 'My Little Secret,' about keeping our relationship under wraps," says Kroeger, 38. "And others like 'Let Me Go,' 'Hush Hush,' and 'Give You What You Like.' Our writing partner must have been like, 'You guys are making me sick!' "
A month and six days after they began dating, Kroeger proposed to Lavigne with a giant, 14-carat rock, and they were wed a year later in July 2013 during a wild, three-day party at a castle in the South of France. They even debuted one of their new love ballads during the wedding.
"We played our duet 'If I Said I Loved You' for our guests and danced to it for our first dance," Lavigne says. "Our guests got to hear an exclusive song! It's our love song," Lavigne says. "We had to play it at the wedding."
So now that they're married, are babies on the agenda? Sure, says Kroeger, just not anytime soon. Lavigne is busy promoting her new album, and Nickelback are about to go on tour to Europe and South Africa.
"We both want it," he says. "We just need to find a time we're both home to get around to it!"
For more on Lavigne and Kroeger, including their rules for making a rock and roll marriage work, pick up the new issue of PEOPLE, on newsstands Friday.