Wilshere, 26, put pen-to-paper with the east London club after his contract expired with Arsenal in July, with both parties unable to agree on a suitable deal.
The central midfielder ended his 17-year association with the Gunners and penned a three-year contract with West Ham, and he made his debut against Preston North End in a friendly on Saturday afternoon.
After unrest last term, the West Ham hierarchy have now supplied new manager Manuel Pellegrini with significant funds to invest in the squad this summer, and the club have signed no fewer than seven players as a result.
The likes of Felipe Anderson from Lazio, Andriy Yarmolenko from Borussia Dortmund and Issa Diop from Toulouse now make up a very exciting team, but Brooking is more enticed by the prospect of free agent Wilshere.
“The player I’m quite excited about is Jack (Wilshere),” Brooking told Sky Sports.
“He’s a talented player, a creative midfielder – West Ham need someone like that to see a pass.
“At 26 – for me the next 5 or 6 years were my best – you’ve got your confidence in your ability.
“And if I was him I’d want to prove to everyone that he can be as good as we know he can be and so for me his presence, if he plays well will be a big plus.”
‘Top 10 a must’
Brooking further believes the investment West Ham have made this summer, along with the appointment of an elite level manager in Pellegrini, should see the club aiming to place in the top half of the Premier League.
He added: “We’ve been looking over our shoulders in the wrong way the last couple of seasons and so we need to get into that top half.
“The top six are really tough to break down but I think this year with the money spent, you’re trying to give the manager the ability to be mid table, top half but then identify where he needs to strengthen the squad if they want to kick on.
“The challenge of the top six is a tough one – you’ve got clubs like Everton and Leicester and West Ham need to be around them this season.”
West Ham start the season with a trip to Anfield on August 12 before hosting Bournemouth the following week at the London Stadium.