Simon Cowell's Baby Mama -- Screw Lawyers ... I Got a Billionaire Divorce Mediator

Simon Cowell's baby mama Lauren Silverman and her ex won't be settling any future disputes through overpaid lawyers -- they've enlisted a trusted mutual friend to hash out their differences ... a man who also happens to be a famous BILLIONAIRE.

According to the divorce settlement, Lauren and Andrew Silverman have named Sir Philip Green as a mediator. Green is the current CEO of the Arcadia Group, which owns the likes of Topshop, and is worth a reported $5.3 billion.

Under the settlement, Green will be one of two mediators (the other being attorney Martin Edelman) for the next 5 years.

We're told the reason Green was named a mediator is because Lauren, Andrew, and Simon each consider him to be a close friend -- and feel comfortable using Green as a neutral go-between.