The Football Association of Wales (FAW) confirmed that former Fulham boss Coleman had been chosen to build on the work of Speed, whose death last November shocked the football world.
However, Coleman acknowledged that his appointment was tinged with sadness following the death of Speed, his former international team-mate and room-mate.
"Whilst on one hand it's probably the proudest moment of my career to be given the opportunity to lead my country, but then to be given that opportunity because of the circumstances nobody could foresee, so it's bittersweet for me, of course it is," Coleman told a news conference.
"I was very close friends with Gary, 30 years, so it's a difficult experience for me. It's probably the most difficult press conference I've ever done or ever had to do, I imagine.
"But I'm very proud to be the new manager and I'm also very sad because of the situation we find ourselves in."
The FAW said Coleman had been chosen after a careful and difficult process.
"All along we believe that we have been respectful and dignified and had no wish to be involved in a public debate on the appointment of Gary's successor," FAW chief executive Jonathan Ford said.
"Gary was the manager of Welsh football and of course we want to continue his legacy. He was not a figurehead, he was the manager, and that is why we have decided on the appointment of Chris Coleman to build on the excellent foundations put in place by Gary."
Coleman, meanwhile, said he hoped to continue the upwardly mobile progress of Wales under Speed.
Wales entered the world's top 50 last year and were the highest rankings climbers of 2011 according to FIFA.
"It's not just the wins but the philosophy and style of play and I think we all agree it's refreshing and we've enjoyed it," Coleman said.
"It was always going to be difficult for the next Wales manager, whoever it was going to be, because of the situation. I think it's even more difficult for me because of my relationship with Gary.
"I've already spoken with the FAW members this morning and I said: 'Excuse me if I don't seem that excited -- I am excited, I'm just a little bit subdued because of the circumstances.'
"It won't be easy but I'm looking forward to it."
Source: AFP
Source: AFP