Matt and Chelsie also took to Twitter to share a video chat to make their announcement.
"Thanks for following us along on this journey. Obviously, I picked Chelsie," Matt said.
"Couldn't be happier with being able to be out in the world without having to hide it all!" the astrophysicist continued with a huge smile.
The reality TV couple said they couldn't wait to begin a 'normal relationship' away from cameras.
"It was so exciting to be able to share our journey with all of you but we're also very excited now to able to do our own normal thing and start a normal relationship," a beaming Chelsie said.
Matt also shared a screenshot to his Instagram story, showing that he was 'finally' following Chelsie.
According to The Daily Mail, Matt and Chelsie weren't permitted to see each other in person since the final episode was filmed, which was in mid-June at the latest.
Last month, Matt told Yahoo that they were on "very, very tight leashes" to avoid spoiling the ending for viewers.