His comments come ahead of tomorrow’s triggering of Article 50, the formal process which will begin talks allowing the UK to quit the bloc.
Sir Simon said while the separation talks could be settled within the two year timeframe, “transitional arrangements” would likely take talks between UK and EU leaders beyond 2019.
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"It's certain that we won't have resolved everything in the period before the expiry of the Article 50 process," the former diplomat told BBC Newsnight.
"The EU side want to start with negotiating the terms of the separation... And the British side, on top of that, wants to move rapidly to discuss the future relationship - both political and economic - between Britain and the EU. And that is a very complex second set of negotiations."
"Any transitional deal, which would likely see a temporary trading relationship while other business is agreed in relations to the future relationships between the two parties, could be necessary to thwart any "risk of political ill will and turbulence - both political and economic", he added.
Mr Fraser was Foreign Office permanent secretary from August 2010 to July 2015.
Although the process to leave the union is agreed at treaty level to be within two years, Mr Fraser suggested that Brexit discussions will not have dominated EU leaders’ discussions thus far, predicting that talks may not begin until autumn following the German elections.
"There has been a very disciplined position across the EU, and I don't think that there has been a lot of informal behind the scenes discussion of the agenda or of the key issues yet," he added.
Sir Simon also suggested that the EU27 will keep a united position on negotiations, adding that “it would be a mistake” for the UK “to try divide and rule” tactics.
Last night David Davis, speaking on BBC Question Time, insisted Britain does have a plan for the scenario of leaving Europe without a final deal.
"We have got a huge contingency plan, exercised across all of these issues, every department of government."
He also insisted that Britain meet any exit bill demands, adding: “We have said before that we will meet our international obligations, whatever that turns out to be.”