They went public with their relationship in September 2018 after walking the red carpet at the E! People's Choice Awards.
Galecki, who has a reported net worth of US$100 million ($136 million), announced in May 2019 he was expecting his first child with Meyer, a model from San Diego.
Galecki was famously in a relationship with his Big Bang Theory co-star Kaley Cuoco for two years during the filming of the show, before they split in 2010.
Johnny Galecki and former co-star Kayley Cuoco dated for years. Photo / Getty
Speaking on Dax Shepard's Armchair Expert podcast last month, Cuoco said she was "crushing so hard" on Galecki when they first met.
"We dated at the beginning of the show for almost two years. When we did the pilot and I was crushing so hard but he had a girlfriend then," said Cuoco, who is married to billionaire heir Karl Cook.
"Eventually, we got together and we were mad about each other for two years but then we broke up.
"Luckily Johnny and I came out of it so brilliantly and we're closer today than we ever were."
On filming sex scenes after their split, Cuoco described how she become suspicious of creator Chuck Lorre.
"It was a little sensitive for a minute. But I just remember Chuck Lorre – the genius behind our show – I remember those weeks where our characters would be jumping in bed with each other every other second.
"Johnny and I talk about it and I think [Chuck] did that on purpose just to f*** with us.
"If I was with him, I would ask him because it came out of nowhere. All of a sudden these characters were all up on each other."
