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The pair, who have been together since 2016, both shared the news on Instagram with the same picture of a diamond ring.
Sophie Turner, who plays Sansa Stark in fantasy TV drama Game of Thrones, posted the photo with the caption "I said yes".
Jonas's brother Nick, who was also in American pop band The Jonas Brothers, tweeted his congratulations.
He said: "Ahh! Congratulations to my brother... and sister in law to be on your engagement. I love you both so much."
The Jonas Brothers was formed in 2005 and gained fame after appearances on the Disney Channel. The band was made up of the three brothers Nick, Joe and Kevin Jonas.
The three-piece broke up in 2013 and Joe Jonas is currently the lead singer for US dance-rock band DNCE.
Sophie Turner, who plays Sansa Stark in fantasy TV drama Game of Thrones, posted the photo with the caption "I said yes".
Jonas's brother Nick, who was also in American pop band The Jonas Brothers, tweeted his congratulations.
He said: "Ahh! Congratulations to my brother... and sister in law to be on your engagement. I love you both so much."
The Jonas Brothers was formed in 2005 and gained fame after appearances on the Disney Channel. The band was made up of the three brothers Nick, Joe and Kevin Jonas.
The three-piece broke up in 2013 and Joe Jonas is currently the lead singer for US dance-rock band DNCE.