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The 7-foot-5-inch center Tacko Fall, who has captivated Boston fans since summer league, will remain in the Celtics’ organization on a two-way contract.

The Celtics on Sunday also agreed to a two-year deal with former two-way contract player Max Strus.

Strus’s new contract has a partial guarantee in the first year and is fully nonguaranteed in the second, according to a source.

“It’s a great opportunity,” Strus said, “but I’ve still got to work and get the last roster spot. Nothing’s for sure yet, so I’ve just got to keep working.”

According to multiple league sources, Strus and the athletic wing Javonte Green are in a tight battle for the Celtics’ final roster spot. One of the two will likely be waived prior to next Wednesday’s season opener against the 76ers.

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Although Green had heretofore outperformed Strus during games in summer league and this preseason, sources said Strus has shined in closed practices. On Sunday, Strus played 16 minutes in Boston’s 118-72 win over the Cavaliers. He made 4 of 5 3-pointers and had 14 points, 4 rebounds, and 2 assists.

“Just a great opportunity,” Strus said. “I took advantage of it. Really thankful for it and had a good game.”

Green, meanwhile, had just 2 points and 2 rebounds in eight minutes.

For the Celtics, part of the impetus for signing Strus to an NBA deal now was that he was willing to add a fully nonguaranteed second year, a league source said. His former two-way contract was for just one year.

Strus’s NBA deal also created a two-way contract opening that the Celtics gave to Fall. Fall will now spend the majority of the season with Boston’s G League affiliate, the Maine Red Claws. He will be able to join the Celtics for up for 45 days during the regular season, too.

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“It’s another opportunity to keep proving myself,” Fall said Sunday. “I’ve worked really hard to get to this point. I’m really fortunate to be in this position, and I’m going to keep fighting to show I can play in the NBA and keep getting better.”

Fall signed an Exhibit 10 contract with the Celtics in June. Under terms of that fully nonguaranteed contract, he would have received a $50,000 bonus if he agreed to join the Red Claws after being waived.

But given Fall’s popularity and potential, Fall likely would have been scooped up by another team if Boston went that route.

By converting his deal to a two-way contract, it ensures that he will remain in the organization.

“We’re happy that he’s with us,” Celtics coach Brad Stevens said, “and I do think that it’ll be good. He just needs to keep working and keep straight ahead and make that the main thing. And he will. He’s a very focused person.”

While many fans have been clamoring for Fall to claim Boston’s final roster spot, a league source said that this situation is preferable for Fall’s long-term future with the franchise.

While his size his tantalizing, some of his skills remain crude, and he now will have an opportunity to play big minutes every night with the Red Claws rather than sit on the end of the bench in Boston.

Also, if Fall had been the 15th man on the regular roster, his spot would have been more tenuous, as he would have potentially been in danger of being released if, for example, Boston made a trade in which it gave up one player in exchange for two.

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Adam Himmelsbach can be reached at adam.himmelsbach@globe.com. Follow him on Twitter @adamhimmelsbach.