Inter, who needed only a draw to secure the trophy on Sunday, moved an unassailable 12 points clear of 2025 champions Napoli with three rounds remaining.
It's Inter's 21st Serie A title, trailing only the record 36 held by Juventus.
Marcus Thuram scored just before the break with an angled shot placed just beyond the reach of Parma goalkeeper Zion Suzuk, then 37-year-old Henrikh Mkhitaryan added another in the 80th after taking a pass from Serie A top scorer Lautaro Martinez, who came off the bench to mark his return from an injury lay-off.
Thuram was born in Parma while his father, Lilian Thuram, also played there.
For Cristian Chivu, Inter's first-year coach, the trophy was secured against the club he coached last season — having helped Parma avoid relegation.
Chivu, who was hired to replace the departed Simone Inzaghi nearly a year ago, played on the Inter team that won a treble under Jose Mourinho in 2010.
In the running for two trophies this season, Inter will next face Lazio in the Italian Cup final in 10 days.
The domestic success has come in sharp contrast to Inter getting knocked out from this season's Champions League play-offs by tiny Norwegian club Bodo/Glimt.
Last season, Inter were routed 5-0 by Paris Saint-Germain in the Champions League final, but this triumph was a big improvement from last season's Serie A when they finished one point behind Napoli.
While Inter were celebrating, AC Milan and Juventus were at risk of losing their Champions League places.
Milan were reduced to 10 men and beaten 2-0 at Sassuolo for their fourth loss in seven matches, before Juventus drew 1-1 with relegated Hellas Verona.
Third-placed Milan are only two points ahead of fourth-placed Juventus, who are three points ahead of fifth-placed Como.
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