The move means work can finally get under way to demolish the derelict block in Incle Street.
Renfrewshire Council has been working for years to secure ownership of the block, next to the site of the former Arnotts store.
A council spokesman said that, at long last agreement had been reached with the remaining owner enabling the council to clear the site.
Work will start in the next two weeks to clear the ground around the flats.
It's expected the block will be demolished over a six-week period starting at the end of November or beginning of December.
Renfrewshire Council Leader Mark Macmillan said: "The council has worked for years to take over this building and I am delighted we have now succeeded.
"It's great news that we can press forward with the environmental and economic opportunities that have now opened up.
"First and foremost, we want to remove an eyesore that blights the main road and rail routes into Paisley.
"Demolishing the building will improve the environment of the town.
"It will also open up a prime location for potential residential or business development."
The flats adjoin the site of the former Arnotts store, where landscaping and improvement work has been carried out to support the marketing of that site for development.
Councillor Macmillan added: "In the medium-term we certainly hope that developers will see the potential of the site.
"For now, we believe the removal of what has been a blot on the Paisley landscape for far too long is a real boost for the town."
The development at Incle Street builds on other successes for the council's Paisley re-vamp ambitions, with new stores announced for the town's former Littlewoods store site, a major new residential investment in Gilmour Street, and the plan for free parking on Saturdays in Paisley town centre backed up by reduced parking charges in the town.