Chelsea are guaranteed European Champions League action next season following their 3-0 win over Watford in the English Premier League on Monday (NZ time).
The news wasn't so good for Manchester United, as their 1-1 draw at relegated Huddersfield Town means they will have to settle for Europa League football next season.
Arsenal will likely have to settle for Europa League action also after they were held 1-1 at home by Brighton.
The results leave Chelsea on 71 points in third place ahead of Tottenham (70), Arsenal (67) and Manchester United (66) with one game remaining.
Arsenal's draw in the late match guaranteed Chelsea of finishing in the top four and a Champions League place, with Tottenham on the cusp of joining them.
Arsenal's hopes hang by a thread due to an inferior goal difference to Tottenham.
"We wanted to win today, and we worked in the Premier League to be with the possibility of getting into the top four, but today we lost the chance," Arsenal manager Unai Emery told Sky Sports.
Goals from Ruben Loftus-Cheek, David Luiz and Gonzalo Higuain lifted Chelsea past Watford at Stamford Bridge.
Loftus-Cheek and Luiz scored three minutes apart early in the second half with Higuain adding some last insurance.
Needing a win, Arsenal and Manchester United both came up empty against teams at the bottom of the table.
Pierre-Emerick Aubameyang put Arsenal in front with a first-half penalty that beat keeper Mathew Ryan at the Emirates Stadium.
But Glenn Murray equalised for Brighton, who only guaranteed their safety last weekend, with a spot-kick of his own in the 61st minute.
Although they could match Tottenham on points, Arsenal would need an eight-goal swing to overtake them.
Earlier, Manchester United's hopes were dashed by a last-placed Huddersfield side that had lost 21 of their previous 23 league games and are destined for relegation.
United were gifted an early opener when Scott McTominay's shot somehow found its way though keeper Jonas Lossl.
But the visitors returned the favour in the second half as Luke Shaw's error sent Isaac Mbenza in to shoot through David de Gea's legs.
Both sides had late chances with United's Paul Pogba hitting the post and Tahith Chong having his shot saved by Lossl, while de Gea denied Karlan Grant at the other end.
"We are where we are for a reason," United manager Ole Gunnar Solskjaer said.
"Over a long season we haven't been good enough to challenge for the Champions League places.
"It's not come as a surprise but we hoped to show a better performance today."