Social media footage showed one person passing urine into a plastic glass before the other threw it towards the travelling supporters at the English national stadium last week.
Tottenham investigated the incident and, after identifying the individuals concerned, have now issued lifetime bans to both men.
"This kind of behaviour is not acceptable and we shall be issuing lifetime bans to both individuals in the video," a Tottenham spokesman said on Monday.
Mauricio Pochettino's side led 2-0 in Wednesday's tie before West Ham hit back to beat their London rivals 3-2 and book a place in the quarter-finals.