Former Sweden boss Lagerback almost led Iceland to a first FIFA World Cup appearance this year, with his side ultimately denied in the two-legged UEFA play-offs by Croatia.
The 65-year-old has now penned a new deal to encompass qualifying for the 2016 European Championship, but Hallgrimsson will step up from his role as assistant to take joint charge before succeeding Lagerback for the next World Cup programme.
Lagerback has previous experience of working alongside another manager, having been joint-coach of Sweden with Tommy Soderberg prior to taking the reins on a solo basis.
At a press conference on Monday, Lagerback said: "I expect to quit after this contract but would like to finish by making it to the Euro finals, even though we are in a difficult group since we will most likely be in the fifth pot of seeds.
Hallgrimsson added: "He (Lagerback) has made me feel like we took this decision together.
"It is good to make a plan for four years and we have a good foundation to build on."
Geir Thorsteinsson, the president of the Football Association of Iceland (KSI), revealed it had been a straightforward decision to extend the contracts of Lagerback and Hallgrimsson.
"I think it has never been easier for the KSI board to sign a coach," he said.
"Lars Lagerback and Heimir Hallgrimsson have support from the Icelandic public, the supporters and of course the players."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.