ABSTRACT With unparalleled rotational stability, millisecond pulsars (MSPs) serve as ideal laboratories for numerous astrophysical studies, many of which require precise knowledge of the distance and/or velocity of the MSP. Here, we present the astrometric results for 18 MSPs of the ‘MSPSR$\pi$’ project focusing exclusively on astrometry of MSPs, which includes the re-analysis of three previously published sources. On top of a standardized data reduction protocol, more complex strategies (i.e. normal and inverse-referenced 1D interpolation) were employed where possible to further improve astrometric precision. We derived astrometric parameters using sterne, a new Bayesian astrometry inference package that allows the incorporation of prior information based on pulsar timing where applicable. We measured significant (${>}3\, \sigma$) parallax-based distances for 15 MSPs, including 0.81 ± 0.02 kpc for PSR J1518+4904 – the most significant model-independent distance ever measured for a double neutron star system. For each MSP with a well-constrained distance, we estimated its transverse space velocity and radial acceleration. Among the estimated radial accelerations, the updated ones of PSR J1012+5307 and PSR J1738+0333 impose new constraints on dipole gravitational radiation and the time derivative of Newton’s gravitational constant. Additionally, significant angular broadening was detected for PSR J1643−1224, which offers an independent check of the postulated association between the HII region Sh 2-27 and the main scattering screen of PSR J1643−1224. Finally, the upper limit of the death line of γ-ray-emitting pulsars is refined with the new radial acceleration of the hitherto least energetic γ-ray pulsar PSR J1730−2304.