Brown, who initially withdrew from consideration for the role before emerging as the favourite after interim coach Todd Payten chose to turn it down, would take over at the end of the 2020 NRL campaign.
On the other hand, Gould will join in a consultancy role to assist the club with strategic direction, while also looking after the development of young talent to help the Warriors "rediscover their mojo".
Australian media have labelled the experienced duo a coaching "dream team".
The 47-year-old Brown has coached the St George Illawarra Dragons, Newcastle Knights and Super League clubs St Helens and Huddersfield, and was one of the first names mentioned as an option for the fulltime Warriors gig after the sacking of Stephen Kearney.
Brown, who joined the Warriors earlier in the year in a consulting role before being cut in the Covid-19 crisis, recently said the Warriors job was a great opportunity.
"I'm a career coach, I love coaching. The Warriors job is a great opportunity as is the Cowboys job," Brown said on Triple M.
"I'm always in dialogue with the Warriors because I work there as a consultant.
"The recruitment officer Peter O'Sullivan is a good friend of mine and we speak quite often."
Brown has coached in 438 games across the NRL and Super League in almost two decades of coaching, with a 50 per cent winning record.
Meanwhile, NRL commentator and former coach Gould's role will be to "overhaul the club's pathways and development systems".
The 62-year-old former player and coach had a similar role with the Penrith Panthers.
When asked about Gould ahead of Friday night's clash against the Manly Sea Eagles, Warriors captain Roger Tuivasa-Sheck said he would add value at any club.
"He brings a lot of wisdom with him, and if the club is looking to bring him on board then I could see it as a positive to have him as a mentor around the club.
"I know he has a big impact in the rugby league community, especially in Australia, so it would be interesting to see the type of work he could do for us.
"That's a decision the organisation would need to make. I'm just focusing on my team here and the players that are here today to make sure we're all ready for a game this weekend."
Gould has a long history in the game as a player, coach, general manager and broadcaster and has recently been in discussions with Australian Rugby League Commission chairman Peter V'landys about undertaking some projects to help the game grow in New Zealand and the Pacific Islands in a development role with the NRL.