The Clyde Bridge was deemed dangerous in August and closed, causing a hail of local protest.
The Ponfeigh Bridge has been out of action since last year due to similar concerns.
Some had given up hope of either bridge ever being brought back into use due to a shortage of funds to repair them.
However, South Lanarkshire Council, in drawing up its budget for next year, has committed £6m to the replacement of both spans, ending months of misery and long diversions for drivers.
The largely unexpected good news was delivered by the council’s chair of Community and Enterprise Resources, Councillor John Anderson.
He said: “The two bridges have been targeted for replacement next year as one of the first acts of a new medium-term capital investment strategy which outlines nearly £400m of spending in the next decade.
“Both bridges had to be closed because our inspections had raised concerns over their safety and obviously that has to be our total priority,” he said.
“However, we knew this would have a significant impact on local people, and those passing through for business or leisure.
“That is why the council has prioritised plans to reopen access at both locations, and I am delighted that we have now been able to confirm our intention to replace both bridges.
“Work will progress as quickly as possible,” he added.