The agreement gives STS the second-highest sponsorship status within the Polish Football Association (PZPN).
STS has sponsored Poland's national team since 2014. Under the new agreement, it will become a strategic sponsor, a position below only the federation's top-level main sponsor.
The financial value of the deal was not disclosed by the PZPN or STS.
The agreement also expands the commercial rights granted to STS. The company will have greater opportunities to use images of Poland players in advertising and will receive additional branding space at national-team matches, including on LED advertising boards and through 3D pitch-side advertising.
Its logo will also appear on the team's training shirts.
STS describes the national team as an important platform for building its brand and maintaining relations with football supporters.
The company currently works not only with the men's national team but also with Poland's women's team and its under-21 and under-20 squads.
STS is also the title sponsor of the Polish Cup and Polish Super Cup and has sponsorship agreements with several Polish clubs.
"Moving up to the status of PZPN strategic sponsor is, above all, an opportunity for us to make even greater use of the potential of the Polish national team in communicating with fans," Dawid Pożoga, STS chief marketing officer, said.
"The new agreement gives us broader opportunities to work with players' images, including in advertising campaigns, as well as increased brand visibility during matches," he added.
For the PZPN, the agreement extends a commercial relationship that has lasted more than a decade.
Polish authorities have recently increased scrutiny of betting companies' practices.
In August, the Office of Competition and Consumer Protection (UOKiK) said it was examining bookmakers' terms and the use of so-called "dark patterns" that could encourage consumers to gamble more frequently or make it harder to stop.
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