Agnew has replaced Bullen as the Sheffield Wednesday caretaker manager.
Bruce was appointed as Jos Luhukay's successor earlier this week, but will not officially take charge until February 1.
Bullen led the Owls to two wins and two draws in a four-game spell as caretaker manager, although it is Agnew who will assume that role in the meantime.
That has raised some concerns over the future of Bullen, who captained Sheffield Wednesday to League One play-off success and later returned as a coach.
But when asked about the popular Scot's involvement, Agnew told the Owls' official Facebook page: "Absolutely, yeah. Lee is very much part of the first-team coaching set-up, and he's an experienced football man.
"He's done terrifically well over recent weeks, he's a great guy, we've already had long conversations upstairs and he'll bring to the table the knowledge of the club, the knowledge of the players and he'll do everything he can to help us and we thank Lee for his help and support."
He added: "Things happen at football clubs that you're not aware of and we'll get to know what's gone on before and how things need to improve and Lee will be very helpful in that apartment."
Despite having been brought to Sheffield Wednesday by Luhukay, with whom he played and worked alongside at VVV Venlo and VFB Stuttgart, respectively, the Dutchman's assistant has also remained at Hillsborough following the appointments of Agnew and Stephen Clemence this week.
"Yeah, Remy (Reynierse) and all the staff are still here," confirmed the 53-year-old. "They've all played an important part in our build-up preparation for tomorrow's game."
Agnew refused to be drawn on the reason behind Bruce's delayed arrival, which the Telegraph claims is due to a knee operation.
How far can Wednesday go under Bruce and co.?