The powerhouse prop – who started for Fiji in both international fixtures with New Zealand this month – moves to the region from French Top 14 side Brive.
Tighthead Doge, 28, has won four caps for his country after making his debut in 2016 against Georgia in Suva.
Dean Ryan, Director of Dragons Rugby, said: “We’re pleased to sign Mesake and look forward to him linking up with us in the coming weeks.
“He’s impressed in the recent Test series with the All Blacks and is determined to come to Wales and develop even further and make a big impression with us.”
Doge – who is 183m tall and weighs 122kg – has been a regular for Brive in the Top 14 making 24 appearances during his two-year stint in France, scoring two tries.
Before that the prop played for Timisoara Saracens between 2017 and 2019, making 27 appearances for the Romanians and scoring three tries.
The Nadogo-born front row joins Dragons with prop Lloyd Fairbrother currently sidelined through injury.
Doge said: “I’m delighted to be joining Dragons. After speaking with Dean and the coaching team, I was very impressed with their vision for the region and their plans for my development.
“To have the opportunity to compete against the very best in the United Rugby Championship and to be joining such a talented squad is truly a blessing. I can’t wait to begin my journey with Dragons.”