Celtic had been in negotiations with the 21-year-old's club, Jagiellonia Bialystok, but they were unable to reach agreement.
On Thursday, the Polish club announced on their official website that they had agreed a fee with Genk and that the player would have a medical on Friday after travelling straight to Belgium following Poland's friendly against Georgia.
Lennon had described Sandomierski as having "huge potential" on Sunday as he reported that the club "might be further down the line" with attempts to sign him.
The Celtic manager has been looking for a goalkeeper to compete with Lukasz Zaluska since Fraser Forster returned to Newcastle following a season-long loan.
Attempts to sign Forster on a permanent deal failed and Lennon did not follow up his initial interest in Stipe Pletikosa after the Croatia international played two friendly matches for Celtic as a trialist.