Eddie Howe's side failed to break the deadlock in a match they dominated, striking the post three times, but the result was sufficient for the Magpies to make a long-awaited return to Europe's elite competition next season.
Newcastle are four points clear of fifth-placed Liverpool heading into Sunday's final day of the season, while Leicester remain in the relegation zone, two points adrift of safety.
The hosts had 78% possession during the contest and initially found it difficult to make inroads, but Callum Wilson hooked an effort against the post and saw his follow-up effort headed off the line by Wilfred Ndidi.
Three minutes before half-time the hosts rattled the post again through Miguel Almiron, while in the second half visiting goalkeeper Daniel Iversen acrobatically tipped over Alexander Isak's effort from distance.
Bruno Guimaraes also hit the woodwork with a header from almost on the goalline in the second period, but Leicester almost won it in injury time when Nick Pope kept out Timothy Castagne's acrobatic effort.
Foxes boss Dean Smith started England internationals James Maddison and Harvey Barnes on the bench but neither was able to inject any impetus into their dull performance after coming on.
Callum Wilson had scored 11 goals in his past 10 games before facing Leicester
It was the 2002-03 season, under the guidance of legendary manager Sir Bobby Robson, when Newcastle last played in Europe's elite club competition.
Howe's men will be back in the big time following a tremendous first full season in charge in which the ex-Bournemouth boss has upset the established order with a place in the top four, as well as taking them to the Carabao Cup final.
It has been a remarkable turnaround since Howe took charge 18 months ago, one month after the Saudi Arabian-backed £305m takeover of Newcastle and with the club five points from safety at the foot of the Premier League.
A tremendous atmosphere was generated by the home fans before kick-off, waving their flags and unfurling a huge banner of Howe and the team, and although they were unable to break the deadlock, they left the stadium singing about Champions League football.
Wilson, who had scored 11 goals in his past 10 games before this encounter, came inches from adding to his tally, while Almiron and Guimaraes also came mightily close.
The Brazil midfielder, though, was lucky to still be on the pitch after receiving only a yellow card for a studs-high challenge on the knee of Leicester midfielder Boubakary Soumare.
Newcastle will aim to complete a successful season on a high on Sunday, travelling to face Chelsea hoping to secure third position.
Leicester host West Ham on the last day hoping the Hammers have taken their eye off the ball with their top-flight place secure and a Europa Conference
League final to look forward to.
But they go into that game knowing even a win might not be enough as 17th placed Everton can guarantee their Premier League status with victory over Bournemouth at Goodison Park.
The result at Newcastle extended Leicester's run to just one win in their past 15 games, earning just seven points during that run, and they are favourites to join Southampton in the second tier.
Supporters will be left wondering how the match may have panned out had key players Maddison and Barnes been given starts instead of being left on the bench.
Castagne's acrobatic effort in the 92nd minute almost secured a shock victory, but their defence did at least manage to keep a first clean sheet in the league since November.