X Factor 2013 champion Bailey's The Power of Love replaces George Michael's Symphonica at the top of the standings, selling nearly 73,000 copies in the process.
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"This really is the icing on the cake to an incredible few months," Bailey - who is expecting her third child later this year - said in a statement to the Official Charts Company.
"I've worked hard to get where I am and I'm so happy that everyone is liking what I'm doing. It really is a dream come true."
Michael's Symphonica drops one place to number two, while Wilko Johnson and Roger Daltrey debut at number three with their collaborative album Going Back Home.
The top five is completed by Pharrell Williams' G I R L and Love in the Future by John Legend.
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This week's Top 40 features several new entries. A 40th anniversary edition of Elton John's seminal album Goodbye Yellow Brick Road debuts at number 12, while Shakira's new eponymous album enters the charts at number 14.
May Death Never Stop You, My Chemical Romance's greatest hits collection, enters at number 15, and Foster the People's Supermodel is new at number 26.
There are also new entries for Tony Bennett and Magnum at 35 and 38 respectively, while Doves frontman Jimi Goodwin enters the charts at number 39 with his debut solo release Odludek.
Source: Official Charts Company
Watch Sam Bailey's music video for her chart-topping single 'Skyscraper' below: