Functional characterization of noncoding sequences is crucial for understanding the human genome and learning how genetic variation contributes to disease. 3' untranslated regions (UTRs) are an important class of noncoding sequences, but their functions remain largely uncharacterized. We developed a method for massively parallel functional annotation of sequences from 3' UTRs (fast-UTR) and used this approach to measure the effects of a total of >450 kilobases of 3' UTR sequences from >2,000 human genes on steady-state mRNA abundance, mRNA stability and protein production. We found widespread regulatory effects on mRNA that were coupled to effects on mRNA stability and protein production. Furthermore, we discovered 87 novel cis-regulatory elements and measured the effects of genetic variation within known and novel 3' UTR motifs. This work shows how massively parallel approaches can improve the functional annotation of noncoding sequences, advance our understanding of cis-regulatory mechanisms and quantify the effects of human genetic variation.