diff --git a/runtime/lua/vim/lsp/util.lua b/runtime/lua/vim/lsp/util.lua
index d2a5d9a08e..0553d39851 100644
--- a/runtime/lua/vim/lsp/util.lua
+++ b/runtime/lua/vim/lsp/util.lua
@@ -724,6 +724,13 @@ function M.rename(old_fname, new_fname, opts)
   local ok, err = os.rename(old_fname_full, new_fname)
   assert(ok, err)
 
+  local old_undofile = vim.fn.undofile(old_fname_full)
+  if uv.fs_stat(old_undofile) ~= nil then
+    local new_undofile = vim.fn.undofile(new_fname)
+    vim.fn.mkdir(assert(vim.fs.dirname(new_undofile)), 'p')
+    os.rename(old_undofile, new_undofile)
+  end
+
   if vim.fn.isdirectory(new_fname) == 0 then
     local newbuf = vim.fn.bufadd(new_fname)
     if win then
diff --git a/test/functional/plugin/lsp_spec.lua b/test/functional/plugin/lsp_spec.lua
index 0fdcd0dd1d..af31d9ccae 100644
--- a/test/functional/plugin/lsp_spec.lua
+++ b/test/functional/plugin/lsp_spec.lua
@@ -2593,6 +2593,58 @@ describe('LSP', function()
         eq('New file', read_file(new))
       end
     )
+    it('Maintains undo information for loaded buffer', function()
+      local old = tmpname()
+      write_file(old, 'line')
+      local new = tmpname()
+      os.remove(new)
+
+      local undo_kept = exec_lua(
+        [[
+        local old = select(1, ...)
+        local new = select(2, ...)
+        vim.opt.undofile = true
+        vim.cmd.edit(old)
+        vim.cmd.normal('dd')
+        vim.cmd.write()
+        local undotree = vim.fn.undotree()
+        vim.lsp.util.rename(old, new)
+        return vim.deep_equal(undotree, vim.fn.undotree())
+      ]],
+        old,
+        new
+      )
+      eq(false, exec_lua('return vim.uv.fs_stat(...) ~= nil', old))
+      eq(true, exec_lua('return vim.uv.fs_stat(...) ~= nil', new))
+      eq(true, undo_kept)
+    end)
+    it('Maintains undo information for unloaded buffer', function()
+      local old = tmpname()
+      write_file(old, 'line')
+      local new = tmpname()
+      os.remove(new)
+
+      local undo_kept = exec_lua(
+        [[
+        local old = select(1, ...)
+        local new = select(2, ...)
+        vim.opt.undofile = true
+        vim.cmd.split(old)
+        vim.cmd.normal('dd')
+        vim.cmd.write()
+        local undotree = vim.fn.undotree()
+        vim.cmd.bdelete()
+        vim.lsp.util.rename(old, new)
+        vim.cmd.edit(new)
+        return vim.deep_equal(undotree, vim.fn.undotree())
+      ]],
+        old,
+        new
+      )
+      eq(false, exec_lua('return vim.uv.fs_stat(...) ~= nil', old))
+      eq(true, exec_lua('return vim.uv.fs_stat(...) ~= nil', new))
+      eq(true, undo_kept)
+    end)
     it('Does override target if overwrite is true', function()
       local old = tmpname()
       write_file(old, 'Old file')