The Premier League club were on Thursday given permission to speak to the former Latics midfielder after agreeing a compensation package with Championship outfit Swansea.
Martinez, 35, was hugely popular in his six years as a player with the club from 1995-2001, when he was one of the 'Three Amigos' along with Isidro Diaz and Jesus Seba.
His stock as a manager has soared over the past year after guiding Swansea to the League One title and then within two places of the Championship play-offs.
Wigan have moved quickly to secure his services after losing Steve Bruce to Sunderland earlier this week.
Whelan told Sky Sports News: "I am delighted and I know the whole of Wigan will be excited we are getting one of the Three Amigos back.
"Roberto played good football and I've followed his career go on and on.
"His players play football from back to front, I like what I see and I am really excited Roberto is coming back to Wigan.
"Compensation was something we had to agree, that is only fair and right. We did that with Birmingham and we have now agreed with the chairman of Swansea.
"Hopefully things will be sorted out and contracts signed by tomorrow morning."
Swansea chairman Huw Jenkins was reluctant to release Martinez and recently rebuffed interest from Celtic.
Whelan, having seen Sunderland swoop for Bruce, admits he can sympathise with the Welsh club.
He added: "Football is a cruel game. Sometimes you don't want to lose a manager, I didn't want to lose Steve Bruce.
"I understand exactly where he is coming from but it is football and things move on."
Reports have suggested the compensation figure agreed is close to £2million.
Whelan said: "It was around that figure. We're both happy anyway - I'll say that."
Swansea are now resigned to losing the highly-rated Martinez, who succeeded Kenny Jackett two years ago.
A statement read: "Swansea City can confirm that they have reluctantly given Wigan Athletic permission to speak to Roberto Martinez about the vacant manager's position at the JJB Stadium.
"Permission was granted when Wigan's offer of compensation reached the appropriate level set by Swansea City, and was only given when taking into account Roberto's own wishes."
Once the appointment is confirmed, Martinez will be given funding to strengthen the Latics squad.
Whelan said: "We are not the biggest club, we have a budget.
"We will talk and we have the money we require to replace players. Roberto will be getting the funds that we can afford to replace the players we need."
Prem W/out Top 4 2009/10 Win Outright: Wigan 100/1