The pair hope to launch tgi50 on 16 August, which is Madonna's 50th birthday.
The company will offer services such as sales promotion, direct marketing, digital, PR, mobile and search-engine optimisation. It does not plan to produce traditional advertising campaigns.
Campbell said: "It's a challenger organisation to Saga. We will be acting as a conduit for contemporary brands that usually aim at under-35s that now want to target the over-50s market but wouldn't be seen dead in Saga magazine."
Campbell and Constantine will be the managing partners of the new venture.
The pair are in talks with a number of brands and venture capital companies in a bid to build interest in tgi50.