Trans-resveratrol (RSV) needs to be encapsulated to maintain its beneficial properties on the human body. This is due to its extreme photosensitivity, short biological half-life, and easy oxidation. In this study, the use of double emulsions for RSV encapsulation and their further application on functional yoghurts was studied. Different types of yoghurts were prepared: with and without RSV and with two types of volumetric emulsion formulations (20/80 and 30/70). In order to study the influence of the addition of double emulsions to the physical properties of the prepared yoghurts, they were characterised fresh and after a month under storage at 4 °C, in terms of droplet size, morphology, stability, rheology, texturometry, colorimetry, and antioxidant capacity. Results obtained showed that the presence of emulsion in the yoghurts produced a generalised decrease in the predominant droplet size (from 48 µm to 15–25 µm) and an increase in the stability. Additionally, a predominantly elastic character was observed. The firmness values obtained were very similar for all the yoghurts analysed and did not suffer important modifications with time. A slight colour variation was observed with storage time in the control sample, whereas a more notable variation in the case of emulsion yoghurts was observed. An appreciable increase of the antioxidant capacity of the final functional yoghurt (100 g) was observed when it contained 5–8 mg of RSV. Encapsulated RSV added to yoghurts presented a larger protection against RSV oxidation compared with free RSV, presenting a larger antioxidant inhibition after one month of storage. Moreover, the antioxidant capacity of yoghurts with encapsulated RSV was not affected under storage, since slight reductions (3%) were registered after one month of storage at 4 °C.