Archer was a second round pick for the Khulna Titans in Saturday’s draft, whilst Wright signed for the Rajshahi Kings back in July.
The 2017 Bangladesh Premier League will take place between November 2 and December 10.
Wright will join Sussex’s former overseas player, Mustafizur Rahman at the Kings.
The Bangladeshi seamer played for Sussex in two matches of the 2016 T20 Blast and was the first pick of Saturday’s draft,