Green’s Dictionary of Slang

certainly, definitely, very much.

1815		T. Whittell ‘The B----p Defeated’s Wedding’ Poetical Works 121: The Right Reverend B----p of D--m well knew it.
1864		Caledonian Mercury 16 June 4/3: We know dam well that you worked a many a bad dark deed.
1870		Taunton Courier 16 Mar. 5/5: You know damn well if you did that the two-thirds of your property [...] would not be worth [etc.].
1881		Freeman’s Jrnl 1 Oct. 3/3: The man was drunk, and did not know what he was saying. Prisoner — I did and damn well.
1912		Bulletin (Sydney) 5 Sept. 16/1: Miss Wowser: ‘And if the Lord came to you now, brother, how would he find you?’ / Bill (who has been losing): ‘Damn well broke, missus!’.
1913		A. Lunn Harrovians 41: Anyhow, you’ve damned well got to.
c.1921		T. Norman Penny Showman 14: It served me damn well right.
1932		(con. 1910s) J.T. Farrell Young Lonigan in Studs Lonigan (1936) 7: He would smoke where and when he damn well pleased.
1939		Dundee Courier 21 Apr. 14/4: You can do what you damn well like, but you can’t make me talk.
1953		R. Chandler Long Good-Bye 227: Ohls laughed. ‘You know damn well why.’ ‘You mean on account of I’m tall, dark, and handsome and somebody might look at me ?’ ‘Cut it,’ Hernandez said coldly. ‘Let’s get on with your statement.’.
1961		R. Gover One Hundred Dollar Misunderstanding 23: I know, I jes dee-diddly-dam well know him an it ain strangers.
1990		(con. early 1950s) J. Ellroy L.A. Confidential 38: Since the county coroner knew damn well who the shooters were, he shipped Mr. and Mrs. Harold J. Scoggins back to Iowa.