It is the first time that Sweden has had representatives in a final of their home ATP tour event in singles or doubles since Elias Ymer and Mikael Ymer won the doubles in 2016.
26-year-old Grevelius is ranked 116th in the doubles world rankings, seven places lower than 24-year-old Heinonen. The pair were wildcards for this event, but battled through two three-set victories to reach the last four, including knocking out fourth seeds Sadio Doumbia and David Pel.
Against Frantzen and Stevens - who dispatched of Swedish number one Andre Goransson and his partner Robert Galloway in the quarter-finals - Grevelius and Heinonen had their most comfortable match of the tournament by far.
They came close to forcing a loss of serve in the opening game but couldn't take either of their two break points, before they had to survive three in game six, yet they responded by taking their chance in the next game, going 4-3 up before wrapping up the set, 6-4.
Having made a fast start in the opener, the Swedes turned the screw in game one of set two, and this time they broke through. They held serve comfortably through the rest of the set before earning another break in game seven, then securing victory with their second match point in game eight to win 6-4, 6-2.
In the final, they will face top seeds Nikola Mektic of Croatia and Edouard Roger-Vasselin of France. The favourites will come into the match well-rested, as they won their semi-final via a walkover against Adam Pavlasek and Patrik Rikl.