Robin van Persie will “evaluate the situation” at Manchester United as he faces the prospect of playing back-up.
Carlo Ancelotti has turned down the chance to return to AC Milan, telling the club he needs rest.
The 30-year-old completed a two-month stint last week at Bristol City where manager Derek McInnes was keen to keep hold of the experienced Liverpudlian.
"I am delighted that we have managed to sign Neil Danns; he is a quality player at this level. He is a strong, physical, creative midfielder who will give our midfield an added edge," boss Simon Grayson told the club's official website.
"He is a highly experienced player who I believe will add to what we already have in midfield. He will also provide us with good versatility in a number of areas."
Danns, who played in all nine of Bristol City's league games after arriving on loan at Ashton Gate in November, signed a three-year deal with Leicester in the summer of 2011 following the expiry of his contract at Crystal Palace.
He was a regular for Leicester in his first season, scoring six goals in 37 appearances, but was sent off twice and did not appear for Nigel Pearson's side after the second of those against Hull in March.
Danns, a product of Blackburn's academy, had loans spells at Blackpool, Hartlepool and Colchester in his early years before making his move to the latter permanent in 2004.
Birmingham paid £500,000 for him 18 months later in the summer of 2006 and Danns completed a £600,000 switch to Palace in January 2008.