Jonas and Turner - who have been dating since November - were first spotted getting close at a concert in the Netherlands and have been inseparable ever since.
Turner had previously admitted dating Jonas can be "frustrating" because of the public scrutiny about their love life.
She explained: "You do feel like you're living in a fishbowl. It's frustrating [that] it's the most mundane things that make the news - how boring!"
And the 21-year-old actress has been desperately trying to keep her relationship with the 28-year-old singer as private as possible.
She shared: "I'm in a relationship, but it's a very private relationship. I'm happier than I've been in a very long time. I very much isolated myself for a while and forgot what was fun. Going out with friends, going out to eat, not really having a care. And people I've met recently in my life have drawn me out of that. It really helps you own those insecurities. The things I tortured myself about before, I can forget about."
Since the news broke, Jonas' brother Nick has rushed to social media to congratulate the couple on their happy news.
Alongside the picture of the ring, he wrote on Twitter: "Ahh! Congratulations to my brother... and sister in law to be on your engagement. I love you both so much. @joejonas @SophieT (sic)"
