The Prime Minister and Taoiseach Micheal Martin have met for the first time since the Fianna Fail leader was elected to the position in June.
The men greeted each other with an elbow bump outside Hillsborough Castle.
"I had the honour of meeting the Taoiseach several year ago," Boris Johnson said.
"I am very pleased to develop our friendship and relationship now."
He added: "It's great to see you Taoiseach, it's great to be here in Northern Ireland and we look forward to developing our relationship in all sorts of ways - east-west, north-south, you name it."
Mr Martin said the relationship between him and Boris Johnson would work "very warmly".
"We look forward to a very warm engagement," he said.
"It is important for us both in terms of the British-Irish relationship which has been the cornerstone of much progress on the island of Ireland and between our two countries for well over two to three decades, and we want to maintain that.
"It is challenging times ahead with Covid, Brexit, all of that."
Mr Martin said it was particularly fitting the engagement was taking place so soon after the death of former SDLP leader John Hume.
"We remember John at moments like this because he did so much to facilitate these kind of meetings and make them much more regular in the normal course of events," he said.
Mr Johnson agreed that the meeting provided an appropriate moment to remember Mr Hume's legacy.
Shortly after arriving at the castle, the Taoiseach joined the Prime Minister for a walk in the grounds.
