I have a pilot license in Brazil and would like to purchase an aircraft in the US and then register it in my country.
My license allows me to fly the aircraft back to my country?
I'm not sure if you're asking about general export regulations, in which case Farhan's link is useful, or the more specific licensing question.
But regarding licensing it's clear that you may not fly a US aircraft from the US to Brazil with only a Brazilian license. 14 CFR 61.3 says:
(a) Required pilot certificate for operating a civil aircraft of the United States. No person may serve as a required pilot flight crewmember of a civil aircraft of the United States, unless that person:
(1) Has in the person's physical possession or readily accessible in the aircraft when exercising the privileges of that pilot certificate or authorization—
(i) A pilot certificate issued under this part and in accordance with §61.19;
(ii) A special purpose pilot authorization issued under §61.77;
(iii) A temporary certificate issued under §61.17;
(iv) A document conveying temporary authority to exercise certificate privileges issued by the Airmen Certification Branch under §61.29(e); or
(v) When operating an aircraft within a foreign country, a pilot license issued by that country may be used.
In other words, you can use your Brazilian license to fly a US aircraft in Brazil (see 61.3(a)(1)(v) above) but otherwise you need a US license or a special authorization (61.77 covers leasing and commercial operations so it almost certainly won't apply to you).
I know very little about this, but at least in theory it looks like your options are:
And those are only the FAA/aviation issues, you have to think about customs and general import/export regulations too, both in the US and Brazil. I would look for some specialized help with this.
With a foreign license you are only allowed to fly aircraft which are registered to the same country as your license in foreign countries. This is the way the international treaty system works.
So, to fly the plane out yourself legally, you would have to get it registered in Brazil somehow first, or get some kind of special permission.
One type of permission is called a "special purpose pilot authorization" (see 14 CFR 61.77). You may be able to get such a special authorization for a one-time flight, even if the aircraft is US registered. If I were you, I would call up the FAA and ask them about it.