The show, which regularly attracts over three million listeners, is Heart's biggest-rating national programme, as the Global Radio-owned station has separate regional broadcasts for its breakfast and drivetime slots.
In January last year, Global Radio rebranded nine of its local stations as Heart, to help attract advertisers with a new national radio proposition.
More Than sponsored a weekend show on Magic FM in 2009, but marketing director Pete Markey said he was keen to secure a weekday programme.
From today, Anstis' show is set to feature a range of promotional activity, both on-air and on the Heart website.
One potential promotion includes offering listeners the opportunities to have a picture of their pet featured on More Than's future pet insurance TV ads.
In addition, Classic FM's weekend afternoon shows will be sponsored by More Than Premier.
The year-long sponsorship ties in with More Than's ongoing music-themed TV campaign, by Fallon, which features tracks by Queen and Simple Minds.
More Than hired MediaVest to its £50m global media planning and buying account mid-way through last year.