It affects both the A55 expressway and the A483 south of Chester.
Overnight closures will be in place from 20:00 BST on Friday on the western side of the roundabout, and the northbound carriageway from Pulford traffic lights.
Restrictions will be in place until 05:00 on Monday.
Highways England, which is overseeing the Â£6m improvement project, said the long-running roadworks were nearing completion and should be finished by 28 June.
During the day on Saturday and Sunday there will be one lane open on the A483 northbound onto the Posthouse Roundabout, however vehicles will not be able to turn right onto the eastbound A55.
Instead, traffic must follow A55 diversions via junction 35.
"We apologise for the delay and disruption in completing this complicated improvement and for the inconvenience these delays have caused to road users on both sides of the border, " said Andy Withington from Highways England.
"We have pulled out all the stops to make sure that the project is completed by Sunday, 28 June - and are still on course to open the road by then."
Work on the roads was originally due to be completed in March, prompting complaints from local politicians on both sides of the Wales and England border.
Motorists are being asked to avoid the Posthouse Roundabout between Wrexham and Chester as planned closures come into force for roadworks.