Mr Robinson stood down on 11 January to face an inquiry over money his wife Iris raised for her former 19-year-old lover.
He announced that his absence could last as long as six weeks while the legal review began the process of clearing his name.
Enterprise Minister Arlene Foster temporarily stood in as First Minister during Mr Robinson's leave.
The DUP leader has continued to lead talks on the transfer of policing and justice powers to Belfast from London.
In tonight's statement, Mr Robinson said of the review by QC Paul Maguire: 'His advice supports my consistent contention that I have acted at all times properly and in full compliance with my public duties.
'I am therefore glad that, at this critical time, I can resume fully the functions of my office with confidence.'
Meanwhile, DUP MP Jeffrey Donaldson has denied there is a split in the party over the devolution of policing and justice powers to Stormont.
Speaking on BBC Radio Ulster, Mr Donaldson said the party was united and unanimous in support of Mr Robinson and its negotiating team.
He said his party will not be intimidated by deadlines.
Mr Donaldson said DUP delegates at the talks wanted to ensure that there was a stable government in Northern Ireland and would not be 'rolled over'.
He said his party was united and that media speculation that 14 DUP members including deputy leader Nigel Dodds rejected proposals in a ballot at a meeting was inaccurate.
DUP MP Gregory Campbell has also strenuously denied speculation that there was a split in the party.
He also disputed press reports that a senior DUP party official had threatened to resign in protest at the proposed agreement with Sinn Fein.
In a separate political development, Ulster Unionist leader Sir Reg Empey has said that rumours of a merger of his party and the DUP were untrue.
Talks between Sinn Féin and the DUP aimed at concluding a deal on the devolution of policing and justice powers have entered their ninth day.
Both parties were involved in discussions at Hillsborough Castle late last night.
'Firm basis for agreement' - Cowen
Taoiseach Brian Cowen has said he believes there is a firm basis for the parties to set a date for devolution of justice and policing.
Mr Cowen told the Dáil that 'inch-by-inch' progress has been made in the talks at Hillsborough and that there is a clear pathway to agreement.
He said he hoped there would be a successful outcome to the talks 'sooner rather than later'.
Fine Gael leader Enda Kenny asked the Taoiseach if he was concerned by stories of a rift inside the Democratic Unionist Party about the agreement on the table. Mr Cowen said such reports were denied by the DUP.
Mr Kenny also asked if there had been a lack of US involvement in breaking the stalemate. The Taoiseach said that the US Secretary of State, Hilary Clinton, had been in touch with the parties.
Labour leader Eamon Gilmore said he had a sense of déjà vu about the current stalemate in the talks.
Mr Gilmore asked if there was too much 'hand-holding' going on where both the Irish and British governments were on permanent stand-by to intervene.
The Taoiseach said that it would ideal if the two parties could find a resolution by themselves but said the governments should be there to assist them.
He also said that the Government should be patient and supportive and said there was a genuine effort being made to find a solution.
Northern Ireland secretary Shaun Woodward told MPs at Westminster that whatever agreement is reached, 'it must be durable'.
He added that 'if we fail we will put the many achievements of the peace process at risk.'
Speaking in the House of Commons, Mr Woodward paid tribute to the leadership of the DUP and Sinn Féin, which he said had been 'in good spirit and in good faith'.
He said that lives had been changed by the peace process but that the parties now sat 'on the edge'.
