According to wikipedia and other sources, a planet and a star always move in a circular orbit around the common center of mass of the both bodies ...
This is not true. In the absence of other gravitational sources, a planet and a star move in elliptical orbits about the common center of mass. Ancient scientists assumed circular orbits, but only because circles were somehow most pure. There were problems with this: It didn't match what those ancient scientists saw. So they modified these circular orbits by tacking on other circles. It was a mess.
Kepler cleaned this mess up by noting that the orbits of the planets are very close to elliptical rather than circular. This empirical result was later strengthened by Newton, who derived that elliptical orbits (not circular orbits) are a natural consequence of a force that follows an inverse square law. Gravitation is such a force.
The orbits of the planets about the solar system are not quite elliptical because planets are attracted to one another as well as to the Sun. Nonetheless, the orbits are still very close to elliptical. The Sun is more than 1000 times more massive than Jupiter. Jupiter, Saturn, and the other planets represent tiny perturbations on the nearly elliptical orbits of the planets about the Sun.
What about other perturbing effects, such as nearby stars and the Milky Way as a whole? These are immeasurably small. A passing star will perturb planetary orbits over the course of the tens of millions of years or more. The Milky Way as a whole has essentially no effect whatsoever. Theoretically, the effect most certainly does exist, but it is so small that it can be ignored, even over the lifespan of the solar system.