And the best pact will lead to more jobs, higher growth and better risk management, said Mark Carney.
In his first public speech since the Prime Minister served the Article 50 notice to quit the European Union, Mr Carney described Brexit negotiations as a "litmus test" for responsible financial globalisation.
He said: "We start from a position where the high road is both readily attainable and highly desirable for all involved.
It is all too easy to give into protectionism, but the road less taken is often the most rewarding
"It is all too easy to give into protectionism, but the road less taken is often the most rewarding.
"All the conditions are in place for following the high road of mutual recognition and cooperation both with Europe and across the G20."
Canadian Mr Carney said the global financial system was at a "fork in the road" and Britain must take the "high road" that builds on the foundations of a "new responsible global financial system that are being put in place".
Mark Carney said Britain and the EU are 'ideally positioned' to agree a deal on financial regulation
The also revealed that the Bank's Prudential Regulation Authority (PRA) has written to all banks and financial firms with cross-border activities between the UK and the EU, including subsidiaries of US investment banks based in London, asking them to prepare for all scenarios in the Brexit negotiations, including a "no deal" outcome.
Mr Carney said: "The main purpose of this letter is to ensure that all firms are making, and stand ready to execute in good time should the need arise, contingency plans for the full range of possible scenarios."
And he also warned of a low road, where "trust and cooperation diminish, fragmentation hardens, capital flows are disrupted and trade and innovation are curtailed".
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Mr Carney said the global financial system was at a "fork in the road"
This path would lead to fewer jobs, lower growth and higher domestic risks.
Theresa May triggered Article 50 last week, kick-starting the two-year process of Britain leaving the EU.
The Governor said there were real risks to financial stability in the transition to the new relationship between Britain and the EU, including disruption of services, a further weakening of investment banking profitability and the potential for greater complexity in firms' legal structures.
Brexit day: images from around the country as Britain invokes Article 50 Mon, April 3, 2017
The country reacts as Theresa May officially invokes Article 50, and begins the process of Britain leaving the European Union
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Pro-EU demonstrators protest outside Parliament
Mr Carney also said there should be no "bonfire of financial regulation" following Brexit.
Asked about the future of the City's politically sensitive euro-clearing operation, Mr Carney said: "There are tremendous economies of scale and scope in clearing multiple currencies in one place.
"We will work hard with EU authorities to ensure the appropriate amount of EU business continues to be cleared in London."
Mr Carney said there should be no "bonfire of financial regulation" following Brexit
The comments come after Manfred Weber, chair of the European People's Party, poured cold water on hopes euro clearing might stay in London after Brexit.
Asked whether the Bank may offer "regulatory sweeteners" to entice banks to stay in the City of London, rather than relocating services to rival EU financial centres, Mr Carney said definitively: "No. Full stop."