They won the promotion from the 1. deild karla in 2008. Stjarnan won the Úrvalsdeild for the first time in 2014.
In the draw for the second round of Europa League qualifying, Inverness were paired with Astra of Romania.
Ronny Deila's side will have to progress through the third qualifying round and a play-off round before they can reach the group stage.
Irish club Dundalk face BATE Borisov, the champions of Belarus.
This is after the initial schedule was reversed to avoid a fixture clash with Andorra's other representatives, Sant Julia, who were also drawn at home to Denmark's Randers in the first leg.
St Johnstone face Alashkert of Armenia, while fellow Scottish side Aberdeen take on Macedonian side Shkendija.
Celtic's Champions League opponents Stjarnan beat Motherwell 5-4 on aggregate in the second qualifying round for the Europa League in 2014-15.
There are no recent events for team Stjarnan Gardabaer
The Scottish champions begin their campaign at Celtic Park on 14 or 15 July with the second leg a week later on 21 or 22 July.
Ungmennafélagið Stjarnan is an Icelandic sports club specialising in football, located in Garðabær,
In Monday's Champions League draw, Welsh Premier League champions The New Saints of Oswestry - one of the seeded teams - were drawn to face B36 Torshavn of the Faroe Islands while Northern Ireland side Crusaders will face Estonian side Levadia Talinn in round one.
Champions Chelsea, second-placed Manchester City and Arsenal, who came third in the English top-flight, have all already qualified for the group stage.
The Bhoys failed to reach the group stage last season, losing 2-1 over two legs to Maribor in the play-off stage.
In the Europa League draw, AUK Broughton meet Lokomotiva Zagreb, while fellow Welsh sides Bala Town and Newtown face FC Differdange 03 of Luxembourg and Maltese side Valletta respectively.
Northern's Ireland's Glenavon play Shakhtyor Soligorsk of Belarus, with Glentoran facing Slovak side MSK Zilina.
The Champions League final is on 28 May 2016 at the San Siro in Milan, while the Europa League finale is on 18 May at St Jakob-Park, Basel.
The association was founded in 1960. The men's division played in 1997 in the first Icelandic League (then Landsbankadeild) and managed the 2006 promotion to the second highest Icelandic league. In 2008 men's reached the summit and thus to play in Úrvalsdeild since 2009.
In the 2014–15 Europa League, they reached the play-off rounds after beating Scottish club Motherwell and Polish team Lech Poznań, before Italian giants Inter Milan denied them a place in the group stages.
Southampton are one of the clubs who will join the Europa League in the third qualifying round draw on 17 July, while English Premier League rivals Liverpool and Tottenham Hotspur qualified directly for the group stage.
They won their first Icelandic league title in style in October, converting a stoppage-time penalty in their final game to beat FH 2-1 and finish one point ahead of their opponents.
Manchester United enter the Champions League in the play-off round, having finished fourth in the Premier League last season.
01.10.2007 - The match between French Metz and Győr decided about the CL place at the end. Győr won by three goals at home.
Cork City will be against KR Reykjavik of Iceland and University College Dublin face F91 Dudelange of Luxembourg.
The Hammers, who qualified for the competition courtesy of their Fair Play record, will play the first leg at Upton Park on 2 July before travelling to an as yet unconfirmed venue in Andorra on 9 July for the return leg.
Should the London club progress, they would come up against either Malta side Birkirkara or Ulisses Yerevan of Armenia.
West Ham start their Europa League campaign against Andorran side FC Lusitans in the first qualifying round.
The club gained worldwide fame when their elaborate goal celebrations, including highly choreographed depictions of landing a fish, diving, a human toilet, a human bicycle, and a Rambo shooting spree, were published widely across the Internet and football television shows.
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The Stjarnan Women play in Iceland's top division, the women's Úrvalsdeild. In 2011 the team won the championship two weeks before the end. The team also reached the final of the Icelandic Women's Cup in 1993 and 2010, losing 1–3 and 0–1 respectively. The team won the cup eventually in 2012 with a 1–0 win over Valur. In 2013 they won their second league title, winning every single game that season thus not dropping a single point.
Shamrock Rovers play Luxembourg's Progres Niedercorn, Linfield tackle NSI Runavik of the Faroe Islands and Saint Patrick's Athletic meet Skonto FC of Latvia.