Castlepoint in Bournemouth opened in 2003 but the two-level car park has been reinforced with props since 2005 when it was found to be unsafe.
Bournemouth Borough Council has granted planning permission for it to be demolished and rebuilt in sections.
Work is expected to be completed by Christmas 2018.
Sean Jeffery, managing director of Kier Infrastructure UK, which built the shopping centre, said: "This is very welcome news. Together with the Castlepoint Partnership, we have worked hard to reach this stage.
"There remain a few key steps to put in place, but this consent brings us closer to being able to start work on-site."
The rebuild has been delayed for years as a result of legal wrangling.
Standard Life Investments, which manages the centre on behalf of Castlepoint Partnership, would not reveal the cost of the rebuild but said there would be no cost to tenants.
To minimise disruption, work will be carried out in five phases, each taking nine to 10 months, stopping for six weeks each Christmas.
Additional parking will be created underneath existing stores to maintain at least 2,500 spaces - the amount needed at peak times.
When the project is complete, the additional spaces will be turned into more shops.
The walkways in front of the upper level stores will also be replaced in phases.

About 300 Jews went to Jasenovac a week ahead of the official ceremony.
Jewish association chief Ognjen Kraus said the snub was a warning to the new centre-right government, which took power in January.
Tens of thousands died at the camp known as the "Croatian Auschwitz".
Ethnic Serbs and anti-fascist groups are also boycotting next week's official ceremony.
The death camp - whose victims included Jews, Serbs and Gypsies - operated under the Ustashe regime, which ran Croatia as a Nazi puppet state.
However, activists say some Croatians see the Ustashe as the country's founding fathers and play down their crimes.
"This is an avalanche that has been rolling for more than a year," said Mr Kraus, president of the Co-ordinating Committee of the Jewish Communities.
In January, ultra-nationalists shouted pro-Nazi slogans at a rally attended by thousands of people, including Deputy Parliamentary Speaker Ivan Tepes.
Similar slogans were also chanted during a football match between Israel and Croatia in March, attended by Prime Minister Tihomir Oreskovic.
Three-quarters of about 40,000 Croatian Jews were killed by the Ustashe and Jews now make up less than 1% of the population.

In an interview marking five years as first minister, Carwyn Jones said people accepted Welsh ministers were not "miracle workers" on NHS matters.
He said Labour had "kept our promises" on health and other issues.
But a Conservative spokesman said the "greatest threat" to Welsh public services was an Ed Miliband government.
Discussing austerity, Mr Jones told BBC Wales: "If we see the Tory plans, we are going to have this until 2020.
"I do not know what the NHS in Wales would look like by 2020, or the education services, if we see those levels of cuts.
"We are just not going to be able to do what we all want to do, so I hope things will change or at least there will be hope in 2015."
In relation to problems in the NHS, he said: "If you are straight with people and say 'look there are problems in some parts of the NHS, money is not there as it was five or six years ago', they accept that.
"They know you are not miracle workers.
"But what you say to people is, we have prioritised those areas we think are important and also, of course, we have kept our promises on health and other areas," Mr Jones added.
A Welsh Conservative spokesman responded: "The greatest threat to Welsh public services is an Ed Miliband government increasing spending and borrowing, leading to crippling interest payments on the national debt, which would significantly reduce the money available to invest in schools and hospitals."
Work to rebuild a shopping centre car park that has been beset with structural problems for a decade will now go ahead in the spring of 2015.
[NEXT_CONCEPT]
Croatian Jews have held their own Holocaust commemoration at a World War Two death camp, in protest at what they say is government inaction in the face of surging neo-Nazi sentiment.
[NEXT_CONCEPT]
It is not known what the state of the NHS or education in Wales will be 2020 if the Conservatives win the general election, the first minister said.