Star Wars confirms Yoda recognized R2-D2 on Dagobah in The Empire Strikes Back. R2-D2 accompanied Luke Skywalker to the swamp world, as Luke sought out the old Jedi Master so he could continue his training. After making camp, the two encounter a strange alien creature, who is later revealed to be Yoda. As a test, Yoda deliberately acted looney and tried to get on Luke's nerves, rummaging through Luke's belongings and attacking R2-D2 with his walking stick.
When The Empire Strikes Back first premiered in 1980, this was simply a comedic moment in the film, but over the past few decades, viewers have raised questions about this sequence. As revealed in the Star Wars prequels and other canon materials, Yoda and R2-D2 were heavily involved with the Republic's efforts to win the Clone Wars, and they even crossed paths on some occasions (most notably Luke and Leia's birth). This made people wonder why Yoda didn't recognize R2-D2 years later when the droid arrived on Dagobah. But, as a matter of fact, he did.
To celebrate The Empire Strikes Back's 40th anniversary, a new anthology book, From a Certain Point of View: The Empire Strikes Back was published. Similar to the From a Certain Point of View that came out a few years ago for A New Hope, it's a retelling of the movie's events from the perspective of various characters. One chapter, detailing Luke's landing on Dagobah, is told from Yoda's point of view. In it, he notices Luke is traveling with a familiar friend:
Carefully moving through the swamp while staying beneath the fog, Yoda soon spotted the boy and his droid unpacking their supplies. Even though the droid was caked with algae, dirt, and stomach fluid, its appearance and familiar blips were still quite recognizable.
R2-D2.
Of course the boy had Anakin's old droid with him. Such cycles of fate no longer surprised the nine-hundred-year-old Jedi.
Most inhabitants of the Star Wars galaxy, even Jedi, do not have deep emotional attachments to droids. During the Clone Wars, Republic astromechs routinely had their memories wiped, but Anakin Skywalker never followed that protocol with R2-D2 because he viewed the little droid as a friend. With that in mind, it is somewhat surprising Yoda knew it was R2-D2 in The Empire Strikes Back just by looking at him - even though they hadn't seen each other for years. Though R2-D2 is an icon amongst Star Wars fans, astromechs are very common in-universe and many of them don't stand out from the crowd. The revelation in From a Certain Point of View makes for a fascinating juxtaposition to a question that came up retroactively in A New Hope, where viewers wondered why Uncle Owen didn't recognize C-3PO. It would appear Yoda is wired more like Luke and Anakin when it comes to fondness for individual droids.
Unfortunately, the entire chapter is told from Yoda's perspective, so it's unknown if R2-D2 recognized Yoda as well. One would imagine he did, since he did not have his memory wiped in Revenge of the Sith, and Yoda has a very distinct appearance and manner of speech. Regardless, it's a great use of the non-movie canon materials to clear this issue up and illustrates the benefits of making a book like From a Certain Point of View. Longtime fans who have debated these very questions now have definitive answers, which should improve rewatches of The Empire Strikes Back.