The plan was outlined during the Queen's Speech on Wednesday.
It means proposals which were already in place to stop MLAs from sitting in the House of Commons will be extended to also prevent them from becoming TDs in the Dail.
Stormont parties have moved to address the issue of double-jobbing however there are still three high profile politicians - Sammy Wilson and Gregory Campbell of the DUP and SDLP leader Alistair McDonnell - who perform two roles.
The cross-border ban comes after a potential loophole was discovered in a draft version of the Northern Ireland bill, published earlier this year by Secretary of State Theresa Villiers.
Ms Villiers intends to outlaw double-jobbing altogether by 2015.