The tracks were recorded before Whitney's death by accidental drowning ahead of the Grammy awards in Los Angeles in February, and will also be included on a new greatest hits album.
Never Give Up has a positive and upbeat message, and includes lyrics such as: "Never, never give up/ Never, never give up/ No matter how many times somebody tells you it ain't working/ Never, never give up.
"Never, never give up/ Hold your head to the sky, look them right in the eyes/ Tell them you will never quit until the day you get it right."
The finances of Whitney's estate are still being worked out, but sales of the new album will help go toward paying back part of a $30-$40 million advance she received for a $100 million record deal signed in 2001.
Whitney's daughter Bobbi Kristina Brown is the sole beneficiary of her mother's estate, and its executors recently reached an agreement with her over payments.
Under the deal, 19-year-old Bobbi will receive 10 per cent of her mother's wealth when she turns 21, almost 20 per cent at age 25 and the remainder when she turns 30.