This crucial development comes as a major blow to the aforementioned Premier League clubs, who were hoping to sign the reliable Switzerland international on a free transfer at the end of the season.
United were reportedly the frontrunners to sign Lichtsteiner, but the new contract in Turin will come as a relief to Rafael, who is likely to remain the Red Devils' first-choice player in the position.
Arsenal were keen following Mathieu Debuchy's ankle injury, but Chelsea also had a strong interest in the player who is widely considered one of Europe's best right-backs.
Relief for Branislav Ivanovic
That Chelsea have been snubbed by Lichtsteiner will come as a huge relief to the Blues' current first-choice right-back, Branislav Ivanovic.
The 30-year-old has been one of the Premier League's most consistent full-backs over the past couple of seasons but faced spending chunks of next term on the substitutes' bench had Chelsea successfully lured Lichtsteiner to Stamford Bridge.
Jose Mourinho is unlikely to pay a transfer fee for a new right-back this summer, with Ivanovic performing so well and Cesar Azpilicueta capable of playing at either left or right-back.
Contract negotiations to re-open?
News of Lichtsteiner's decision could convince Chelsea to re-open negotiations with Ivanovic, who was reportedly on the verge of signing a new four-year contract last March before contract talks stalled months later.
Arsenal were subsequently linked with a move to Ivanovic, but Arsene Wenger opted instead to sign France international Debuchy from Newcastle United for an undisclosed fee.
Ivanovic would have no shortage of potential suitors should Chelsea fail to offer him a new deal - but the Blues' supporters will expect Jose Mourinho to get the Serbia international tied down to a new long-term deal following six seasons of excellent service.
Juventus bidding for another league title
Lichtsteiner, meanwhile, follows in the footsteps of Paul Pogba, Arturo Vidal and Andrea Pirlo by committing his future to the reigning Serie A champions.
Juventus currently sit top of the Italian league table and remain on course to secure a fourth successive Serie A title.