London Olympian Smith was the favourite before dislocating her shoulder at the GB Championships earlier this month.
A statement from British Weightlifting said Smith would undergo shoulder surgery to return to full fitness.
Tiler, who won the GB 69kg title at the trials - is joined by Sonny Webster who competes in the men's 94kg class.
"I've been struggling with injury since the beginning of the year which has seriously hindered, and eventually ended, my road to Rio," Smith said.
"Although I'd obviously rather be competing, I'm glad I can give myself the break from competing that my body clearly needs."
It will be a first Olympic Games for Tiler and Webster, who were both crowned British Champion in their respective weight categories earlier this month.
Two years ago, Tiler finished fourth at the 2014 Commonwealth Games - aged just 15 - and earlier this year she won three bronze medals at the European Championships in Norway.
Webster also competed at the Commonwealth Games, finishing fifth, and is a former European junior bronze medallist. The 22-year-old broke the British U23 record at the 2016 British Championships, with Tiler breaking two British records on their way to the titles.
Team GB have won seven Olympic weightlifting medals - one gold, three silver and three bronze - with the last medal won at Los Angeles 1984 when David Mercer took home bronze.
Rebekah Tiler has won the battle for Britain's sole female weightlifting place at the Rio Olympics after Zoe Smith failed to recover from injury.