My answer has two parts, Conditions, and Solution.
Part I: Conditions
I had the same problem, but I had already a similar repository with the same structure,
say 
Project1 (not a repo)
   |___ Repo1
   |___ Repo2
and:
Project2 (a repo)
   |___ Submodule1 (same repo as Repo1)
   |___ Submodule2 (same repo as Repo2)
And I wanted to convert Repo1 and Repo2 to a submodule of Project1 that it is basically the same as Project2. 
To state clear, cloning Project2 would not do the  trick because there were a lot more files in Project1 and Project2 that were not the same, but to keep things simple..
So my Project1's .git/config looked like this
[core]
repositoryformatversion = 0
filemode = false
bare = false
logallrefupdates = true
symlinks = false
ignorecase = true
And my Project2's .git/config like this:
[core]
    repositoryformatversion = 0
    filemode = false
    bare = false
    logallrefupdates = true
    symlinks = false
    ignorecase = true
[submodule]
    active = .
[remote "origin"]
    url = ######
    fetch = +refs/heads/*:refs/remotes/origin/*
[branch "master"]
    remote = origin
    merge = refs/heads/master
[submodule "Submodule2"]
    url = ######
[submodule "Subodule2"]
    url = ######
and in Project2, there was a file called .gitmodules:
I had the same problem, but I had already a similar repository with the same structure,
say 
Project1 (not a repo)
   |___ Repo1
   |___ Repo2
and:
Project2 (a repo)
   |___ Submodule1 (same repo as Repo1)
   |___ Submodule2 (same repo as Repo2)
And I wanted to convert Repo1 and Repo2 to a submodule of Project1 that it is basically the same as Project2. 
To state clear, cloning Project2 would not do the  trick because there were a lot more files in Project1 and Project2 that were not the same, but to keep things simple..
So my Project1's .git/config looked like this:
[core]
    repositoryformatversion = 0
    filemode = false
    bare = false
    logallrefupdates = true
    symlinks = false
    ignorecase = true
And my Project2's .git/config like this:
[core]
    repositoryformatversion = 0
    filemode = false
    bare = false
    logallrefupdates = true
    symlinks = false
    ignorecase = true
[submodule]
    active = .
[remote "origin"]
    url = URL/TO/Project2
    fetch = +refs/heads/*:refs/remotes/origin/*
[branch "master"]
    remote = origin
    merge = refs/heads/master
[submodule "Path/To/Submodule2"]
    url = ######
[submodule "Path/To/Subodule2"]
    url = ######
and in Project2, there was a file called .gitmodules:
[submodule "Path/To/Submodule1"]
    path = Path/To/Submodule1
    url = ######
    branch = master
[submodule "Path/To/Submodule2"]
    path = Path/To/Submodule2
    url = ######
    branch = master
So what to do:
Part II: Solution
- Ensure that submodules have the same folder name
Project1 (not a repo)
        |___ Submodule1
        |___ Submodule2
- Then copy - Project2/.gitmodulesto- Project1/
 
- Then copy the content submodule part of Projec2's - .git/conifto Project1's- .git/configthat it basically look like Project2, but not overriding [remote "origin"]:
 
And my Project1's .git/config like this:
[core]
    repositoryformatversion = 0
    filemode = false
    bare = false
    logallrefupdates = true
    symlinks = false
    ignorecase = true
[submodule]
    active = .
[remote "origin"]
    *url = URL/TO/Project1*
    fetch = +refs/heads/*:refs/remotes/origin/*
[branch "master"]
    remote = origin
    merge = refs/heads/master
[submodule "Path/To/Submodule2"]
    url = ######
[submodule "Path/To/Subodule2"]
    url = ######