The 20-year-old defensive midfielder, who also has a club option for a further year built into his new Brentford terms, has made 10 substitute appearances in the Premier League since joining the Bees from Sivasspor in January 2024.
He spent the second half of last season on loan at Oxford United in the Championship, making 16 appearances in a campaign that ended in relegation to League One.
Lincoln sporting director Jez George described Konak as the club's "number one" summer target for the midfield, pointing to his defensive attributes as the key selling point.
"As a number six, we feel as though all his out of possession attributes fit perfectly to our game model and that we can help him to develop some of his other qualities in how we play with the ball," George told the Imps' official website.
Brentford's decision to extend Konak's contract before loaning him out reflects the value the west London club places on his long-term development. He made his professional debut for Sivasspor as a 17-year-old in August 2023 and started the following 16 league games, form that earned him a place among the Guardian's list of the best young talents in world football born in 2006.
Konak arrives at Lincolnshire just three days after the club began life back in the Championship for the first time in 65 years with an opening-day defeat to Middlesbrough. The Imps are next in action at home to Portsmouth on Saturday.
For Brentford, the move continues a pattern of tying down promising young players to fresh terms before sending them out for regular first-team football elsewhere. Konak was included in the club's matchday squad for the final game of the 2023-24 season against Newcastle United before making his senior bow as a late substitute in a Carabao Cup win over Colchester United the following August, and later made his Premier League debut away at Tottenham Hotspur.