The rights group said the two countries had together sent more than five billion dollars (4.6 billion euros) worth of arms to Riyadh since a Saudi-led coalition intervened in Yemen in March 2015.
That was more than 10 times their humanitarian aid to Yemen during the same period, it said.
The London-based watchdog described the alleged arms transfers as a "shameful contradiction" of aid efforts by the United States and Britain.
"These governments have continued to authorise such arms transfers at the same time as providing aid to alleviate the very crisis they have helped to create," said Lynn Maalouf, Amnesty's deputy director of research for the Middle East and North Africa.
"Yemeni civilians continue to pay the price of these brazenly hypocritical arms supplies."
In March 2015, Saudi Arabia and its Gulf allies launched an air campaign to support Yemen's president against Shiite Huthi rebels who had seized control of northern Yemen and the capital Sanaa.
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More than 7,700 civilians have since been killed and a further 40,000 wounded, according to the United Nations. Seven million Yemenis now face starvation, it says.
The United States has become increasingly involved in the conflict since Donald Trump took office in January.
The Pentagon says it has carried out 40 air raids this month against Yemen-based Al-Qaeda in the Arabian Peninsula.
The Saudi-led Arab coalition has come under repeated criticism over civilian casualties in Yemen.
Earlier this month, Amnesty accused the Saudi-led coalition of using banned cluster munitions in raids on residential areas.
Amnesty said the bombs, made in Brazil, had been used in multiple attacks since October 2015, most recently last month in the Huthi-controlled northern Saada region.
In December the coalition admitted it had made "limited use" of British-made cluster bombs. It maintains it does not deliberately target civilians.