The NA62 experiment reports the branching ratio measurement BR(K+→π+ννˉ)=(10.6−3.4+4.0∣stat±0.9syst)×10−11 at 68% CL, based on the observation of 20 signal candidates with an expected background of 7.0 events from the total data sample collected at the CERN SPS during 2016-2018. This provides evidence for the very rare K+→π+ννˉ decay, observed with a significance of 3.4σ. The experiment achieves a single event sensitivity of (0.839±0.054)×10−11, corresponding to 10.0 events assuming the Standard Model branching ratio of (8.4±1.0)×10−11. This measurement is also used to set limits on BR(K+→π+X), where X is a scalar or pseudo-scalar particle. Details are given of the analysis of the 2018 data sample, which corresponds to about 80% of the total data sample