The singer's sixth studio album, his first since 2010, outsold its nearest rival - Bon Iver's 22, A Million - by 4,500 copies.
David said: "Thank you so much from the bottom of my heart. I don't know what's going on right now."
He described scoring the second number one album of his career with Following My Intuition as "the most amazing feeling".
David had last hit the top spot with Born To Do It in 2000.
"I'm seeing two generations connecting - the people who have been with me since 1999 and the crew who are just discovering me, both connecting on the same music," he said.
All of the top four albums this week were new entries.
My Universe by The Shires debuted at number three, becoming the fastest-selling album by a British country music act in chart history.
Van Morrison's Keep Me Singing, the singer's 36th studio album, entered at number four.
Radiohead rounded off the top five with A Moon Shaped Pool, which leapt 80 places up the chart after a new deluxe edition was released.
In the singles chart, X Factor winner James Arthur held on to the number one spot for a second week with Say You Won't Let Go.
Starboy by The Weeknd featuring Daft Punk rose to number two, while The Chainsmokers featuring Halsey's Closer dropped a place to three.
Calvin Harris's My Way held its number four position, while Side To Side by Ariana Grande featuring Nicki Minaj rose one place to break the top five for the first time.
Further down the top 10, One Direction's Niall Horan scored his first chart hit as a solo artist, with his debut single This Town landing at number nine, following a surprise release last Thursday.
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Craig David has scored his first number one album for 16 years.