McVeigh was appointed Essendon coach on Monday, with the club opting for the Sydney Swans assistant ahead of fellow former Bombers player Hird, Fremantle's Jaymie Graham and Adelaide's Murray Davis.
Hird, who quit as Essendon coach in 2015 after a tenure marred by the club's supplements saga, had pitched for the top job.
"I feel there is significant value James can bring," Welsh told reporters of Hird on Tuesday.
"Not just tokenistic, but real value James can bring to our club and playing group."
Hird didn't answer Welsh's calls, and the Essendon president sent him a text and hoped to speak with his former teammate on Tuesday.
Hird was an assistant to McVeigh when he was interim GWS senior coach in 2022.
"I love James Hird, he's one of my best mates," McVeigh said.
"It was difficult to go through the process against a good friend.
"I don't fear those people (Hird supporters), I actually embrace how they feel. And I understand it to be fair.
"He's been a constant in my life ... we spoke this morning. It hasn't broken us, we're still together."
McVeigh added he speaks regularly with Hird and will discuss the prospect of a role at Essendon.
"I need to understand where his footy journey is going to go from here," he said.
There has been murmurings of a board spill already from Essendon fans, disgruntled Hird didn't get the job.
"I sit here year after year and we get people coming out of the shadows that want to challenge the board," Welsh said.
"I can tell you, since I've been here, this club has never been more united.
"So these people want to keep living in the shadows and come and try and destabilise our club. We don't jump at shadows.Â
"We're a strong club, and we'll continue to make sure that we're making the right decisions on behalf of our members and our teams and our staff to get this club moving forward again."
McVeigh wants ex-caretaker coach Dean Solomon, who was on hand at the announcement, on his coaching team and said the pair had laughed off any suggestion of tension between them.
"Absolutely want Dean Solomon as part of the group," he said.
McVeigh was one of the banned "Essendon 34" and couldn't fulfil his role as an assistant at the Giants during his suspension.
The supplements saga has hung over the club for years, but their new coach was adamant he could drive the Bombers past it.
"We're not going to live in the past. It's about now. That was a long time ago," McVeigh said.
"Tested my resilience, so it helps. But yeah, we won't live in the past. We're here for the now. This is what we're about now.
"This is who we're going to be."
McVeigh described himself as a "no ego" coach as he bids to lift the Bombers from the abyss after they collected the wooden spoon in 2026.
"I want to bring the club back to where it needs to be," he said.
McVeigh has only briefly met champion midfielder Zach Merrett, who is expected to seek a trade to Hawthorn for a second straight year.
"You must respect your champions. I'm big on that," McVeigh said.
"Zach and I will sit down at the appropriate time.
"I think it's really important we understand the player's feelings. It's not just about the club's feelings, it's about his feelings and where he's at.
"I respect him. I want him to be here, but I'll listen to him as well."
