According to E! News, fans spotted a very pregnant Anna in a gynaecologist waiting room with Jesse, and took pictures which ended up on multiple fan accounts.
The couple originally started dating back in 2002, and were together for 10 years before splitting in 2012.
Jesse then briefly dated co-star Mia Wasikowska, whom he met while filming The Double, before rekindling his relationship with Anna after a four-year break in January 2016.
Before starring in London's The Spoils at the start of January 2016, Jesse managed to raise over £400k for Middle Way House, the domestic and sexual abuse shelter in Indiana, US, that Anna's mother is the director of.
His donation meant that the shelter could pay off their mortgage, and it's been suggested as the possible reason behind why the pair reunited that month. The fact that Anna and her family are so charitable is one of the things that attracted Jesse to his girlfriend, as she and her mother work on multiple projects to help others.
'I find people who want to help other people to be the most interesting,' he said.
'I come from a family of teachers, and my friends are teachers, often times in very difficult school situations.
'My job is so selfish and focused on my own vanity that I like to surround myself with people who are actually helping people throughout their day.'
In 2011, Jesse told Seventeen that Anna was the only woman he'd ever gone on a date with, and that the secret to their long relationship was simply that they try to be as nice to each other as often as they can.
Jesse has starred in The Social Network as Facebook founder Mark Zuckerburg, in Woody Allen's film Cafe Paris as well as Batman vs Superman: Dawn of Justice.
We look forward to more news of this couple's happy addition, and wish them the best of luck!