He was born in Australia but is qualified to play for Ireland through his ancestry and has won 32 international caps.
He represented the British & Irish Lions in the summer and played 35 minutes for the tourists in their win over the Melbourne Rebels.
Commenting on his reasons for leaving Ulster, Court said: "I feel that this is the right decision with regards to me and my career at this stage.
"It is going to be very sad when the time comes to actually leave and finish up, but there is a lot of rugby left for me with the province.
"There are six months remaining of this season, so there is even more motivation for me to make the most of it while I am here and to try and help Ulster win something."