According to the agreement, which was unveiled at a press conference on Wednesday morning, Sweden will contribute five JAS Gripen fighter planes as well as a naval boarding team.
"We're going to present a bill tomorrow morning," foreign minister Carl Bildt said during a Wednesday morning press conference announcing the agreement.
"There will be more surveillance operations that what we've been able to achieve so far."
He added that the Swedish mission in Libya could continue even after a ceasefire.
Bildt was joined by Social Democrat foreign policy spokesperson Urban Ahlin and Green Party spokesperson Åsa Romson to announce details of the agreement.
"Most people clearly believe that today is not the day to stop supporting Libya's civilians and it's not the day to end the no-fly zone," said Romson.
"It's time to increase the humanitarian mission and help with the refuges situation."
Exactly how large the boarding team will be is up to the Swedish Armed Forces (Försvarsmakten) to determine, as is exactly which type of soldiers are best suited for the job.
On Tuesday, Left Party leader Lars Ohly released preliminary details about the agreement following a briefing with Bildt, even though his party would not be a part of the deal.
He said the Swedish team of soldiers tasked with boarding ships would fall under British command.
According to Ahlin, the force could be in place within a few days following a formal Riksdag decision on the matter.
The current Swedish mission in Libya consists of a squadron of eight Gripen fighters sent to enforce a UN-mandated no-fly zone which came into force on March 17th.
Officials from NATO, which took over responsibility for the foreign military mission in Libya on March 31st, have asked the Swedish government to extend the Gripen surveillance mission.
The deal comes following weeks of uncertainty about whether the government could strike a deal with the Social Democrats after an April 28th interview with the TT news agency in which party leader Håkan Juholt ruled out keeping the Sweden's Gripen aircraft in Libya.
On May 18th, the party proposed extending Sweden's military presence in Libya, but with a naval contribution rather than simply supporting the no-fly zone.
On Monday, however, Ahlin said the Social Democrats were open to allowing one or two planes to remain in Libya.
The agreement means that during a visit to Brussels on Wednesday, defence minister Sten Tolgfors can tell his NATO colleagues exactly what Sweden is prepared to offer.
NATO has proposed extending the current military mission in Libya another 90 days from July 1st.
An extension of the mission requires a new bill to be presented in the Riksdag before June 22nd.
The previous agreement on the current mission included all political parties except the far-right Sweden Democrats.