We present the 90-μm luminosity function of the Final Analysis of the European Large Area ISO Survey (ELAIS), extending the sample size of our previous analysis (Paper IV) by about a factor of 4. Our sample extends to z= 1.1, ~50 times the comoving volume of Paper IV, and 107.7 < h-2L/Lsolar < 1012.5. From our optical spectroscopy campaigns of the northern ELAIS 90-μm survey (7.4 deg2 in total, to S90μm>= 70 mJy), we obtained redshifts for 61 per cent of the sample (151 redshifts) to B < 21 identified at 7 μm, 15 μm, 20 cm or with bright (B < 18.5) optical identifications. The selection function is well-defined, permitting the construction of the 90-μm luminosity function of the Final Analysis catalogue in the ELAIS northern fields, which is in excellent agreement with our Preliminary Analysis luminosity function in the ELAIS S1 field from Paper IV. The luminosity function is also in good agreement with the recent IRAS-based prediction of Serjeant and Harrison - which, if correct, requires luminosity evolution of (1 +z)3.4+/-1.0 for consistency with the source counts. This implies an evolution in comoving-volume-averaged star formation rate at z<~ 1 consistent with that derived from rest-frame optical and ultraviolet surveys.