The Scots were drawn in Group 1 of League C.
They will begin the tournament with a home match with Albania on Monday 10 September, before travelling to Israel just over a month later on Thursday 11 October.
The group will then conclude with a double-header. Scotland will visit Albania on Saturday 17 November and then conclude the group by hosting Israel three days later.
Scotland have never faced Albania, and have played Israel just three times - all in the 1980s.
Scotland played Israel twice in the 1982 World Cup qualifiers, winning 1-0 in Tel Aviv thanks to a Kenny Dalglish goal before a 3-1 victory at Hampden, courtesy of a John Robertson penalty brace and a goal from Davie Provan, with Moshe Sinai grabbing a consolation for Israel.
The last meeting between the two sides was a friendly match in 1986, with Paul McStay scoring the only goal in a 1-0 victory at the Ramat Gan Stadium in Tel Aviv.
Scotland and Liverpool left back Andy Robertson said: “It was exciting to watch the Nations League draw play out.
“It’s been a while since Scotland have played Israel and we’ve got a good record to defend.
“There are a few well-known names in their squad and the Celtic lads, I’m sure, will be giving Nir Bitton a bit of stick about it when the time comes.
“I think I’m right in saying that we’ve never played Albania before, so that will be something different for the squad and supporters alike.
“They did well to get to the last Euros and are clearly a nation on the up.
“It’s something to look forward to. Pulling on the Scotland shirt always means the world to me and we’re determined to get to a major tournament.
“The Nations League is something that could take us there and we’ll put everything into it.”
The other groups in League C saw Hungary, Greece, Finland and Estonia making up Group 2, Slovenia, Norway, Bulgaria and Cyprus in Group 3 and Romania, Serbia, Montenegro and Lithuania in Group 4.
In Group 3 of League B, Northern Ireland were drawn to face Bosnia & Herzegovina and Austria while the Republic of Ireland are in Group 4 of League B along with Wales and Denmark.
Engalnd face Spain and Croatia in Group 4 of League A.
The first round of matches will take place between September 6th and 8th 2018.
The Nations League competition will see semi-finals, the final and a third-placed game, held between June 5-9, 2019.
The 16 Nations League group winners will go into play-offs for Euro 2020, to be played in March 2020. If they have already qualified for the European Championship the next best-ranked team in their league will take their place in the play-offs.
Each league has a path of its own, and will consist of two single leg semi-finals and a one-off final. The winner of each path qualifies for Euro 2020.
At the end of the group stages of the Nations League, those who finish bottom of the groups will be relegated to the league below and four teams will be promoted to the league above.