Mr Kennedy was a long-time champion of healthcare reform
The Massachusetts state senate has voted to allow the state's governor to pick an interim replacement for the late US Senator Edward Kennedy.
Under current rules, Mr Kennedy's seat would remain vacant until a special election could be held.
Massachusetts Governor Deval Patrick is expected to approve the rule-change and pick Mr Kennedy's successor this week.
Former Massachusetts governor and presidential candidate Michael Dukakis is the frontrunner for the job.
The rule-change was one of Mr Kennedy's last wishes.
If his seat remains vacant, the Democrats will only have 59 votes in the Senate, one short of the 60 needed to overcome the Republicans' procedural blocking tactics.
The late senator feared that if his fellow Democrats did not have a full complement of senators, passing a healthcare reform bill would be more difficult.
Mr Kennedy campaigned throughout his career for universal healthcare, and did not want his death to jeopardise prospects for reform.
Massachusetts's current rule requiring a special election to fill a Senate vacancy was only brought in in 2004 by the state's Democrats.
They feared that if then-presidential candidate John Kerry had won that year's presidential election, thus vacating his Massachusetts senate seat, his replacement would have been chosen by then-governor Mitt Romney, a Republican.
The current proposed rule-change is likely to be accompanied by a resolution strongly urging the appointed senator not to run in the 2010 special election, which will determine who will be Mr Kennedy's permanent replacement.