The Anglo-Italian team announced three key hires on Monday afternoon as it goes through a significant revamp under incoming team principal Laurent Mekies.
In addition to Goss and Permane coming in, it has also hired Red Bull aerodynamicist Guillaume Cattelani as its deputy technical director.
Goss has been brought in to report to Mekies in the newly-created position of chief technical officer, following his recent departure as the FIA's technical director for single-seaters.
Goss, who previously worked at McLaren from 1990 to 2018, will take up his new role in October, nine months after leaving the FIA.
"I am delighted to join Visa Cash App RB at the start of its new era of competition," said Goss.
"It's a team with great pride and heritage, with some exceptional people already in place, and I'm looking forward to working with team principal Laurent Mekies and alongside technical director Jody Egginton.
"There's an exciting challenge ahead of us but I think the team is well-equipped to meet that head-on."
As previously reported by Motorsport.com, the team has also appointed former Alpine man Permane as its racing director to oversee all of its trackside operations, a similar role he had been fulfilling at the Enstone team until his dismissal last July.
"After a few months of downtime, it's great to return to racing again with the Visa Cash App RB team," Permane added.
"From long experience, I know how professional, driven and competitive the people within this race team are and I can't wait to see where that spirit can take the team in the future."
Finally, Cattelani has been brought in from sister team Red Bull to work as a deputy to technical director Egginton.
According to Egginton, Cattelani's "focus on aerodynamics and vehicle dynamics will allow us to hone and develop this year's car and add capability going forward, while Tim's arrival will absolutely give us the structure we need to create cars that will elevate the team's performance even further in the coming years."
Over the past three years, Cattelani has been a chief engineer for Red Bull, having joined Milton Keynes in 2020 after a six-year tenure as McLaren's head of aerodynamics and a shorter stint with Lotus.
Commenting on the signings Mekies said: "The appointments of Tim, Guillaume and Alan add a vast amount of winning expertise to the team, and I have no doubt that they will help take the team to the next level in F1.
"We already have a very strong and hugely experienced group at the team and bringing onboard highly-skilled individuals like Tim, Guillaume and Alan will boost our capability and help us meet the highest technical standards, both at the factory and at the track."
