The breakthrough cleared the way for a special summit in Brussels on Sunday, at which leaders of the remaining 27 European Union states are expected to give their stamp of approval to both the future framework and a separate withdrawal agreement setting out the terms of the UK's departure.
He backed Mrs May to get a deal through parliament, saying: "If I were a betting man - and I fancy a bet every now and then - I think she'll get it through".
Last year's European Union guidelines on the Brexit negotiations effectively gave Spain veto powers over future relations between the bloc and the British overseas territory, and the Spanish government says it will vote against the Brexit deal if Gibraltar's future isn't considered a bilateral issue between Madrid and London.
Asked if the PM's deal was worse than remaining in the bloc, Raab told BBC Radio 4's Today programme: "I'm not going to advocate staying in the EU".
May's office said she would meet European Commission President Jean-Claude Juncker in Brussels on Wednesday as part of work to finalize the declaration.
British critics of the deal believe it binds Britain too closely to Europe-wide regulations while leaving it with no say in formulating those directives.
The political declaration, seen by AFP, says future ties will be wide-ranging, covering economic cooperation, law enforcement and criminal justice, foreign policy, security and defence.
In the event of a no-deal Brexit, the UK's trading relationship with other countries will be governed by World Trade Organisation (WTO) rules.
The prime minister also refused several times to say whether she would resign if she loses the upcoming parliamentary vote on her deal.
The prime minister told MPs the future relationship document is a good deal for Britain, ending free movement once and for all and introducing skills-based immigration.
May said she will give a statement on the latest in negotiations at the House of Commons Thursday evening and travel to Brussels on Saturday ahead of the emergency Brexit summit, which is set for Sunday.
He added: "It could be no deal, but it could be no Brexit, we just don't know". Conservative rebels have vowed to defeat the prime minister while the Northern Ireland DUP, which props up her minority government, has threatened to break its deal with the prime minister.
We could still try and negotiate a post-Brexit free trade agreement with the European Union in a no deal scenario, it's just that without the withdrawal agreement, and the transition period, the UK's relationship with the European Union will be very different immediately after March 2019.
Downing Street said the prime minister was holding a teleconference with cabinet ministers about the deal.
They also warned that "if the political declaration is not unanimous, there is no declaration", alluding to a draft text on the future relationship that will also be voted on Sunday.