Achara averaged 10.6 points and six rebounds per game during EuroBasket and earned his 50th GB cap in the side's home game at the Copper Box in London at the start of their preparation period.
Meanwhile, point guard Andrew Lawrence also signed in Eastern Europe last week in his first professional deal with Croatian side, KK Zadar.
After graduating from Charleston University and enjoying a strong summer with the senior men's GB team once again, Lawrence begins his professional career with the side who finished 12th in the Adriatic League last season.
Dan Clark will return to the ACB this season after agreeing a short term deal with Laboral Kutxa over the weekend. Clark will play with GB team mate, Devon van Oostrum at the Spanish side after a strong performance for GB at EuroBasket where he averaged a team-high 12.6 points per game.
Elsewhere, Myles Hesson and Ali Fraser already have contracts in Germany while Drew Sullivan and Gareth Murray will play for sides in the BBL.
British Basketball National Teams Director, Warwick Cann commented: "We are very pleased that more of our players have their professional contracts agreed. Kieron, Dan and Andrew are all key players for GB moving forward and all played very well at EuroBasket.
"I am sure they will gain further from their clubs and come back in to the national team in great shape and with enhanced skills and experience."