The Prime Minister has said that maintaining strong trading links is vital to ensuring Brexit is a success.
On Thursday, May will then make her way to Paris to meet with French President Francois Hollande.
Though she has spoken with both on the phone already, these will the first face-to-face meetings, and could set the tone of future negotiations around Brexit.
French and German national elections are next year, and with the growing presence of populist parties (Front National and Alternative for Germany), both leaders are under pressure to deliver a hard bargain to the UK.
May has said she wants to build a strong personal relations with her counterparts, and emphasis the value of economic and security relations with countries of the EU.
"These visits will be an opportunity to forge a strong working relationship that we can build upon and which I hope to develop with more leaders across the European Union in the weeks and months ahead," she said.
"I do not under-estimate the challenge of negotiating our exit from the European Union and I firmly believe that being able to talk frankly and openly about the issues we face will be an important part of a successful negotiation.
"I also want to deliver a very clear message about the importance we attach to our bilateral relationship with our European partners, not just now but also when we have left the European Union.
"These relationships have been vital in the past and they will be vital in the future as we continue to work together to keep our people safe and to support economic growth that benefits people across our countries."
On the agenda is also the refugee crisis and the fallout from the failed Turkish coup over the weekend.
The Prime Minister has said that talks of Britain's exit of the EU should be frank and open, though informal discussions have been prohibited until formal talks can begin when Article 50 is triggered.
Former foreign secretary Philip Hammond said to a select committee hearing, before he moved job, that while bureaucrats in Brussels were eager for Article 50 to be triggered soon, there was more understanding among fellow nations and their leaders that more time could be needed.
Lawyers acting on behalf of the government told the high court yesterday morning that Article 50 will not be triggered in 2016.
Last week the Prime Minster, during a trip to Scotland, also said she would not trigger Article 50 until a UK wide approach was agreed.
Meanwhile, May, during her first cabinet meeting yesterday, told her colleagues that while "Brexit means Brexit", the government will not be defined singularly by it, but by its social reforms as well.