Tavernier, 22, is expected to go straight into Steve Evans' squad for this weekend's home game against Gillingham and will stay with the Millers until January 2.
"He is a very accomplished full-back, who can play on either side of the pitch and if needed can step in and do an excellent job at centre-back if required," Evans told the club's official website.
"With the injury to Mark Bradley, and Rob Milsom, who covers us at left-back also having a minor injury issue, this an excellent signing for us.
"This is a young man who I have watched develop over the last couple of years and I have taken the time not only to watch him in the first-team at Newcastle United, but also when he has appeared on loan at other clubs," Evans continued.
"I must also acknowledge and thank Alan Pardew at Newcastle United, and obviously his assistant Steve Stone, who has helped myself persuade the young man to join us in preference to a number of other alternatives he had."
Tavernier, who has had previous loan spells at Carlisle, Sheff Wed and Shrewsbury, has made nine appearances for Newcastle, but has yet to appear for them this season.
On Bradley, Evans added: "Mark is probably going to be away for three to four weeks. He had a scan and it's shown the injury in his groin is a little bit deeper than we thought so that's going to be three to four weeks. It will put pressure on us."