The agreement between Canberra and London will scrap almost all taxes on Australian products entering Britain, including meat, dairy, sugar and wine.
Taxes on 90 per cent of Australian goods exported to India, including meat, wool, cotton, seafood, nuts and avocados, will also be removed.
The agreements were passed by parliament on Tuesday.
Trade Minister Don Farrell said the agreements will help Australia reach its full economic potential
"More trade, not less, is a key part of how we build the economic future we want in Australia with secure, high-paying jobs," he told the Senate on Tuesday.
Senator Farrell said the agreement with India provides the opportunity for a second tranche of trade negotiations for greater access to a market of 1.4 billion people.
Prime Minister Anthony Albanese intends to lead a trade and business delegation to India early next year.
Opposition foreign affairs spokesman Simon Birmingham said the agreements created "a vibrant network ... to enable Australian businesses to succeed in the world".
The agreements will not automatically come into effect once they pass the Australian parliament, with both needing to be ratified by the respective partner nations.
Senator Farrell has spoken to both the Indian and UK governments to alert them to the passing of the legislation.
The UK's legislation is currently before a parliamentary committee, with no outlined reporting date.
The Indian deal only requires the ratification of the government's cabinet, and the trade minister is hopeful that can take place within a couple of weeks.
"So all of the benefits that flow from the India free trade agreement should be available to Australian producers this year," Senator Farrell told ABC TV.
"Unfortunately, the English system is slightly more truncated. I'm still hopeful we might get it this year, but it may be early next year."
The trade minister is also working to remove billions of dollars worth of Chinese trade sanctions, but acknowledged there is some way to go, despite thawing diplomatic relations.
"We'll continue those discussions and try to resolve all of our outstanding issues with the Chinese government," Senator Farrell said.
"There's a benefit for both countries to resolve this issue."
Senator Farrell used a meeting with World Trade Organisation director-general Ngozi Okonjo-Iweala on Tuesday to announce an additional $5 million over four years for developing nations.
The funds will help the least developed nations realise the benefits of WTO membership.
16°C