Jenkins was born and raised in DeKalb, Illinois. His mother, Mary Elizabeth (née Wheeler; 1914–2003), was a housewife, and his father, Dale Stevens Jenkins (1916–1997), was a dentist. He attended DeKalb High School. Before he was an actor, Jenkins drove a linen truck (his boss was actor John C. Reilly's father). Jenkins earned a degree in Drama from Illinois Wesleyan University before relocating to Rhode Island.

Jenkins and his wife, Sharon R. Friedrick, were married on August 23, 1969. They have two children, son Andrew Dale and daughter Sarah Pamela, and reside in Cumberland, Rhode Island.

Since his debut in the television movie Feasting with Panthers (1974), Jenkins has been working steadily in film. His earlier film credits include Hannah and Her Sisters (1986), The Witches of Eastwick (1987), Sea of Love (1989), How to Make an American Quilt (1995), Flirting with Disaster (1996), and Snow Falling On Cedars (1999).

He has worked with the Director siblings the Farrelly brothers in There's Something About Mary (1998), Outside Providence (1999), Me, Myself & Irene (2000), Say It Isn't So (2001), Hall Pass (2011) and the 2012 Three Stooges remake. He has also appeared in three Coen Brothers movies: The Man Who Wasn't There (2001), Intolerable Cruelty (2003), and Burn After Reading (2008). He is in North Country (2005), has three memorable scenes as FBI Director James (Robert) Grace in The Kingdom (2007), and Step Brothers (2008).

Jenkins is perhaps best known for playing Nathaniel Fisher in the HBO drama series Six Feet Under. His character is the deceased patriarch of the Fisher family and regularly appears to his family as a ghost or in dreams. He played the role for the show's entire run. He and his castmates received a Screen Actors Guild Award nomination for Outstanding Performance by an Ensemble in a Drama Series in 2002.

Although primarily known for supporting parts, Jenkins had a lead role in The Visitor (2007) for which he was nominated for the Independent Spirit Award and an Academy Award for Best Actor. Jenkins won the International Press Academy's Satellite Award for Best Actor – Motion Picture.

In 2010, Jenkins costarred in Dear John, as the father of John Tyree (Channing Tatum), and also co-starred with Julia Roberts and Javier Bardem in Eat Pray Love. In 2012, he appeared in the Joss Whedon and Drew Goddard horror film The Cabin in the Woods and the action film Jack Reacher. He then appeared in the action films White House Down (2013) and Kong: Skull Island (2017).

In 2014, Jenkins and his wife Sharon received the Pell Award for Lifetime Achievement from Trinity Repertory Company in Providence.

In 2015, Jenkins won the Primetime Emmy Award for Outstanding Lead Actor in a Miniseries or Movie for his performance as Henry Kitteridge in the HBO miniseries Olive Kitteridge.

Jenkins co-starred in Guillermo del Toro's fantasy romance drama film The Shape of Water (2017), for which he received critical acclaim. For his performance, he garnered Academy Award, Golden Globe and Screen Actors Guild Award nominations for Best Supporting Actor.