diff --git a/lld/ELF/Writer.cpp b/lld/ELF/Writer.cpp
index 321599b0055ae3..0069822d12178b 100644
--- a/lld/ELF/Writer.cpp
+++ b/lld/ELF/Writer.cpp
@@ -2597,9 +2597,10 @@ static uint64_t computeFileOffset(OutputSection *os, uint64_t off) {
     return alignTo(off, os->ptLoad->p_align, os->addr);
 
   // File offsets are not significant for .bss sections other than the first one
-  // in a PT_LOAD. By convention, we keep section offsets monotonically
+  // in a PT_LOAD/PT_TLS. By convention, we keep section offsets monotonically
   // increasing rather than setting to zero.
-   if (os->type == SHT_NOBITS)
+  if (os->type == SHT_NOBITS &&
+      (!Out::tlsPhdr || Out::tlsPhdr->firstSec != os))
      return off;
 
   // If the section is not in a PT_LOAD, we just have to align it.
diff --git a/lld/test/ELF/linkerscript/tls-nobits-offset.s b/lld/test/ELF/linkerscript/tls-nobits-offset.s
index 8a774aec0d64f7..9aab32317be4cc 100644
--- a/lld/test/ELF/linkerscript/tls-nobits-offset.s
+++ b/lld/test/ELF/linkerscript/tls-nobits-offset.s
@@ -11,17 +11,16 @@
 ## p_offset will be set to the sh_offset field of the section. Check we align
 ## sh_offset to sh_addr modulo p_align, so that p_vaddr=p_offset (mod
 ## p_align).
-## TODO: Currently we fail to ensure this, as shown by this test
 
 # CHECK:      Name  Type     Address          Off     Size
 # CHECK-NEXT:       NULL     0000000000000000 000000  000000
 # CHECK-NEXT: .text PROGBITS 0000000000000000 000190  000000
 # CHECK-NEXT: .sec1 PROGBITS 0000000000000000 001000  000001
-# CHECK-NEXT: .tbss NOBITS   0000000000000400 001001  000001
+# CHECK-NEXT: .tbss NOBITS   0000000000000400 001400  000001
 
 # CHECK:      Type Offset   VirtAddr           PhysAddr           FileSiz  MemSiz   Flg Align
 # CHECK-NEXT: LOAD 0x001000 0x0000000000000000 0x0000000000000000 0x000001 0x000001 R   0x1000
-# CHECK-NEXT: TLS  0x001001 0x0000000000000400 0x0000000000000400 0x000000 0x000001 R   0x400
+# CHECK-NEXT: TLS  0x001400 0x0000000000000400 0x0000000000000400 0x000000 0x000001 R   0x400
 
 # CHECK:      00 .sec1 {{$}}
 # CHECK:      01 .tbss {{$}}
diff --git a/lld/test/ELF/tls-nobits-offset.s b/lld/test/ELF/tls-nobits-offset.s
index 9dbff0d52b4b5c..9bfbedab6c78c2 100644
--- a/lld/test/ELF/tls-nobits-offset.s
+++ b/lld/test/ELF/tls-nobits-offset.s
@@ -7,13 +7,12 @@
 ## p_offset will be set to the sh_offset field of the section. Check we align
 ## sh_offset to sh_addr modulo p_align, so that p_vaddr=p_offset (mod
 ## p_align).
-## TODO: Currently we fail to ensure this, as shown by this test
 
 # CHECK: Name  Type   Address          Off     Size   ES Flg Lk Inf Al
-# CHECK: .tbss NOBITS 0000000000211000 000158  000001 00 WAT  0   0 4096
+# CHECK: .tbss NOBITS 0000000000211000 001000  000001 00 WAT  0   0 4096
 
 # CHECK: Type Offset   VirtAddr           PhysAddr           FileSiz  MemSiz   Flg Align
-# CHECK: TLS  0x000158 0x0000000000211000 0x0000000000211000 0x000000 0x000001 R   0x1000
+# CHECK: TLS  0x001000 0x0000000000211000 0x0000000000211000 0x000000 0x000001 R   0x1000
 
 # CHECK: 02 .tbss