News of the appointments had been leaked to the media earlier in the week but Farrell gave the rubber stamp in London on Wednesday.
Easterby filled in for Farrell as interim Ireland coach during the Six Nations Championship and had been expected to stay in charge for the summer Tests against Georgia and Portugal, but instead joins the Lions as defence coach.
Ireland backs coach Goodman will look after the Lions' attack, with Fogarty in charge of scrums.
Former England scrumhalf Wigglesworth, No.2 to England head coach Steve Borthwick after following him to Twickenham from Leicester, and Scotland forwards coach Dalziel complete the lineup.
After their back to back Six Nations wooden spoons, there will be no Wales coaches involved for the first time since 2001.
Farrell had already announced the appointment of David Nucifora (General Manager, Performance), Aled Walters (Head of Athletic Performance and Vinny Hammond (Head of Analysis).
"This coaching group has versatility and are interchangeable in their skillset, which is a vital asset to have on a Lions Tour," said Farrell, who will name his playing squad on May 8 in an event at London's 02 attended by thousands of fans for the first time.
"I think we have a fantastic mix and every one of these guys will bring their own character and personality to the team."
Easterby, brought up in England but who played club rugby in Wales and internationals for Ireland and the Lions on their 2005 New Zealand tour, looks an ideal fit.
"I was lucky enough to tour with the Lions 20 years ago. It's been a long time between gigs, but it is an exciting time and I am looking forward to getting stuck in," he said.
"To tour as a player and now as a coach, knowing the group of players that we have the potential of working with, is something that I can't wait to get stuck into."
Wigglesworth is England's sole representative on the coaching team.
"Proud is probably an understatement to how I am feeling right now. I never got to play with Andy, but he was my coach at Saracens and England so I know his calibre and I am thoroughly looking forward to working with him," he said.
The Lions get the tour underway against Argentina in Dublin on June 20.
They then play five warm-up matches in Australia before the three Tests on July 19, July 26 and August 2.
The Lions won their last series in Australia 2-1 in 2013 having lost the previous series 2-1 in 2001.
Their last tour was under COVID conditions in South Africa in 2021, when they lost 2-1.
