The South African – who has made 115 appearances for Dragons - makes the move to south west France with immediate effect and links up with former Dragons fly half Dorian Jones at the Stade Chanzy outfit.
Landman, 32, moved to the Dragons in the summer of 2014 after previous playing spells with South African teams Leopards, Lions, Boland Cavaliers, Griquas and reached the Super Rugby play-offs whilst with the Cheetahs in 2013.
The second row made his competitive Dragons debut against Connacht in September 2014 and was later made captain at the region.
Landman said: “After 93 starts in 115 appearances for the Dragons in the last four years, the time has come for me to continue my journey elsewhere for the next three months.
“My family and I would like to thank everyone that made us feel so welcome since we arrived in this beautiful rugby loving country.
“I am grateful for the opportunity the Dragons gave me to come over and explore rugby in the northern hemisphere and furthermore for agreeing my loan to help me to pursue my rugby goals further.
“Thanks to all the awesome Dragons fans for the non-stop support through the good and bad times. Diolch yn fawr.”
Interim Head Coach Ceri Jones said: “Rynard has made a big impression at the region with over a century of games during his time at Rodney Parade.
“We have agreed to this loan deal to France to allow him to explore this new opportunity.
“On behalf of everyone at the region, we wish Rynard well during his time with Angouleme.”