Amazon's store, named "Amazon MP3," allows users to buy music without copy protection technology, so that the songs can play on a variety of devices including Apple's iPod.
Most songs are priced from 89 cents to 99 cents, with more than half of the 2 million songs priced at 89 cents, the online retailer said in a statement.
Many Web start-ups have proposed business models to take on iTunes, which has a 70 percent market share of digital music sales. Many have also failed as they get caught up in negotiations with the music companies.
For weeks Amazon had been expected to launch its iTunes rival after signing deals with Universal Music Group, which is owned by French media giant Vivendi, and EMI.
U.S. music companies, concerned about piracy enabled by file-sharing Web site, are mulling new business models with a goal of increasing digital revenue as CD sales drop more sharply than anticipated.
They also hope to create alternatives to iTunes to boost their negotiating power against Apple when licensing contracts are renewed.