Mr Johnson said Stormont could now "move forward with improving people's lives".
They have both signed up to a deal, tabled by the United Kingdom and Irish governments, that offered compromise resolutions to a range of long-standing disputes on issues such as the Irish language.
The main Irish nationalist and pro-British unionist parties in Northern Ireland have agreed to return to a power-sharing government after a three-year hiatus, ending a stand-off that had threatened a key part of the province's 1998 peace settlement.
"It's time to Get Northern Ireland Moving Forward Again".
Mr Varadkar, Mr Johnson and others are expected in Belfast from 10.30am onwards.
Johnson was in Northern Ireland to meet with the leaders of the power-sharing executive, which was restored over the weekend after three years of deadlock.
Northern Ireland's smaller parties pledged their commitment to making the Stormont Assembly work, despite an "imperfect" draft deal.
Iran says missile attacks on USA targets were 'legitimate self-defense'
American President Donald Trump's first answer until the attack it was "all is well" and "so far, so good". Assessment of victims and damage that is now taking place.
The centrist Alliance party and its leader, Naomi Long, will now head the police and courts department because unionists have insisted that Sinn Féin can not control the Department of Justice given of his past association with the IRA.
Mr Johnson said discussions at Stormont would focus on how the executive meant to take forward "critical reforms" to public services.
Equal marriage has finally become legal in Northern Ireland, with same-sex couples able to register to marry for the first time from Monday, January 13.
Speaking on BBC Radio Ulster's Nolan Show on Monday morning, DUP agriculture minister Edwin Poots suggested that domestic rates may have to be increased to provide additional money and the introduction of a water charge could be possible.
Last week the British and Irish governments helped broker a deal restore the Assembly. The pro-British Democratic Unionist Party has endorsed the plans to restart the institutions, which collapsed in February 2017 over a renewable energy initiative that spiralled far over-budget.
The central government has promised to inject hundreds of millions of pounds into the NHS of Northern Ireland in the aftermath of the political agreement that led to the re-establishment of decentralized government.
Photo by William Cherry/Presseye Prime Minister Boris Johnson (left), First Minister, Arlene Foster of the DUP (centre right), deputy First Minister Michelle O'Neill (centre left) of Sinn Fein, and Secretary of State for Northern Ireland, Julian Smith (right) during their visit to Stormont, Belfast.