Hammond said that there is a trade off between market access and restrictions on movement, which need to be agreed at the start of negotiations and not the end, meaning a "steady hand" is needed.
Writing in the Telegraph, the Conservative minister said: "To make that early progress will require a steady hand, a steely nerve, good judgement, a clear understanding of our own political limitations and a finely tuned appreciation of the position of, and political restrictions on, our negotiating counterparts.
"But most of all it will require a good dose of old-fashioned British pragmatism. The time for dogmatic rhetoric is past; the decision to leave is made.
"But the deal we get, and with it Britain's economic future, will depend on the qualities of the next Prime Minister. That is why I am supporting Theresa May as the person best equipped to secure our nation's interests in these challenging times."
He added: "I do know this: to get the best deal, we will need our next Prime Minister to approach this process with a pragmatic, not a dogmatic, mindset."
Theresa May is now the clear favourite to win the Conservative crown, with the backing of many more MPs than her competitors.
However, Michael Gove, Andrea Leadsom, Stephen Crabb and Liam Fox have all thrown their hats into the ring.
The leadership race was thrown open after Prime Minister David Cameron said he would stand down following the government's failure to win the referendum.
Hammond added that the UK needs to "engage effectively with the EU27 to establish a sound basis on which the UK can co-operate with its European neighbours, on trade, on security, on defence and foreign policy, in educational and research collaboration and, crucially, in respect of rights and restrictions on freedom to work, study and settle in each other's territory".
Secondly, he wrote, the UK needs to develop a plan to reshape its own economy to reflect the new reality outside the EU. That is in part because of the trade off that Hammond sees as inevitable.
"Those who believe there is no need for such a trade-off have misunderstood something fundamental about the politics of the EU," Hammond continued.
"They have a principled belief in the "indivisibility of the four freedoms"; but they also have a political understanding that to give way to Britain on this question would likely lead to the unravelling of the EU. So we will need to come to a consensus as a nation on that central trade-off."
There is a range of outcomes between "no access" and "full unfettered access" to the market, with a range of corresponding outcomes on free movement, he said.